ࡱ> BD?@AIAgu%` ebjbjNN bl,,`W::::rrr$^^^Pb $l '4(446>Wk $khn rM  ::46W| : 4 r66<r*6  '$^0,A?bA*Ar*w]*www  ^www$:::::: Algebra 3 Assignment Sheet WELCOME TO TRIGONOMETRY, ENJOY YOUR STAY (1) Assignment # 1 ( Complete the circle diagram (2) Assignment # 2 ( Sine & Cosine functions chart (3) Assignment # 3 ( Other Trig functions chart (4) Assignment # 4 ( Finding other trig functions (5) Assignment # 5 ( Review Worksheet (6) TEST (7) Assignment # 6 ( Angle Addition Formulas (8) Assignment # 7 ( Double, Half-Angle Formulas (9) Assignment # 8 ( Review Worksheet (10) TEST (11) Assignment # 9 ( Trig Identities (1) (11) Assignment # 9 ( Trig Identities (2) (12) Assignment # 10 Problems ( 1 9 ) ( Solving Trig Equations (13) Assignment # 10 Problems ( 10 18 ) ( Solving Trig Equations (14) Assignment # 11 ( Review Worksheet Solving Trig Equations (15) TEST INTRODUCTION TO TRIGONOMETRY I Definition of radian: Radians are an angular measurement. One radian is the measure of a central angle of a circle that is subtended by an arc whose length is equal to the radius of the circle.  Therefore: arc length = angle in radians x radius  The radius wraps itself around the circle  EMBED Equation.DSMT4  times. Approx. 6.28 times. Therefore  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Dividing you get  EMBED Equation.DSMT4 .. EMBED Equation.DSMT4  Conversely ... EMBED Equation.DSMT4   Ex. Change  EMBED Equation.DSMT4  to radians. Change  EMBED Equation.DSMT4 to degrees. Convert the following from degrees to radians or vice versa: 1.  EMBED Equation.DSMT4  2.  EMBED Equation.DSMT4  3. 195 EMBED Equation.DSMT4  4.  EMBED Equation.DSMT4  5.  EMBED Equation.DSMT4  6.  EMBED Equation.DSMT4  II UNIT CIRCLE: The unit circle is the circle with radius = 1, center is located at the origin. What is the equation of this circle? Important Terms: A. Initial side: B. Terminal side: C. Coterminal angles: D. Reference angles: The initial and terminal sides form an angle at the center if the terminal side rotates CCW, the angle is positive if the terminal side rotates CW, the angle is negative   unit circle positive negative coterminal Coterminal angles have the same terminal side& . -45 and 315 or  EMBED Equation.DSMT4  and  EMBED Equation.DSMT4  The reference angle is the acute angle made between the Terminal Side and the x-axis    III GEOMETRY REVIEW 30  60  90 EMBED Equation.DSMT4  RIGHT TRIANGLES 45 45 - 90 EMBED Equation.DSMT4     Therefore, for the Unit Circle, hypotenuse is always 1.   Algebra 3 Assignment # 1  Trigonometric Functions Let   theta represent the measure of the reference angle. Three basic functions are sine, cosine and tangent. They are written as sin , cos , and tan  Right triangle trigonometry - SOHCAHTOA  EMBED Equation.DSMT4    EMBED Equation.DSMT4    EMBED Equation.DSMT4  A. Find cos  B. Find sin        C. Find tan  D. Find sin  Triangles in the Unit Circle  On the Unit Circle: I  Where functions are positive  II Reference Triangles A. Drop  EMBED Equation.DSMT4 from point to x-axis.   B. Examples 1. Find sin  EMBED Equation.DSMT4    2. Find cos EMBED Equation.DSMT4  Same as cos EMBED Equation.DSMT4    3. Find sin  EMBED Equation.DSMT4  =   4. Find cos  EMBED Equation.DSMT4  =   5. Find sin  EMBED Equation.DSMT4  = cos  EMBED Equation.DSMT4  = III Quadrangle Angles Def: An angle that has its terminal side on one of the coordinate axes. To find these angles , use the chart  Find the sine, cosine for all the quadrangles.  EMBED Equation.DSMT4   HYPERLINK "Trigonometry.gsp" Trig values Algebra 3 Assignment # 2 Complete each of the following tables please. Radian Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 SinCos Radian Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 SinCos Answers Radian Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure EMBED Equation.DSMT4  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Sin EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1 EMBED Equation.DSMT4  EMBED Equation.DSMT4 0 EMBED Equation.DSMT4 Cos EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 0 EMBED Equation.DSMT4  EMBED Equation.DSMT4 (1 EMBED Equation.DSMT4  Radian Measure EMBED Equation.3  EMBED Equation.DSMT4  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure EMBED Equation.DSMT4  EMBED Equation.3  EMBED Equation.DSMT4  EMBED Equation.3  EMBED Equation.DSMT4  EMBED Equation.3  EMBED Equation.DSMT4  EMBED Equation.3 Sin10 EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 1Cos0(1 EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4  EMBED Equation.DSMT4 0 6.2 Other Trigonometric Functions  Sin( Cosecant: Cos( Secant: Tan( Cotangent:  HYPERLINK "http://mathplotter.lawrenceville.org/mathplotter/mathPage/trig.htm" http://mathplotter.lawrenceville.org/mathplotter/mathPage/trig.htm Find the following values 1. EMBED Equation.DSMT4 2. EMBED Equation.DSMT4 3. EMBED Equation.DSMT4 4. EMBED Equation.DSMT4 5. EMBED Equation.DSMT4 6. EMBED Equation.DSMT4 7. EMBED Equation.DSMT4 8. EMBED Equation.DSMT4 6.2 Algebra 3 Assignment # 3 Complete the following tables. Radian Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure330(450((135(240(SinCosTanCotSecCsc Radian Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure540(150((210(270(SinCosTanCotSecCsc Answers Radian Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure480(330(135(450(30((135(900(240(Sin EMBED Equation.3 ( EMBED Equation.3  EMBED Equation.3 1 EMBED Equation.3 ( EMBED Equation.3 0( EMBED Equation.3 Cos( EMBED Equation.3  EMBED Equation.3 ( EMBED Equation.3 0 EMBED Equation.3 ( EMBED Equation.3 (1( EMBED Equation.3 Tan( EMBED Equation.3 ( EMBED Equation.3 (1Undef. EMBED Equation.3 10 EMBED Equation.3 Cot( EMBED Equation.3 ( EMBED Equation.3 (10 EMBED Equation.3 1Undef. EMBED Equation.3 Sec(2 EMBED Equation.3 ( EMBED Equation.3 Undef. EMBED Equation.3 ( EMBED Equation.3 (1(2Csc EMBED Equation.3 (2 EMBED Equation.3 12( EMBED Equation.3 Undef.( EMBED Equation.3  Radian Measure EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Degree Measure(270(540((420(150(585((210(315(270(Sin10( EMBED Equation.3  EMBED Equation.3 ( EMBED Equation.3  EMBED Equation.3 ( EMBED Equation.3 (1Cos0(1 EMBED Equation.3 ( EMBED Equation.3 ( EMBED Equation.3 ( EMBED Equation.3  EMBED Equation.3 0TanUndef.0( EMBED Equation.3 ( EMBED Equation.3 1( EMBED Equation.3 (1Undef.Cot0Undef.( EMBED Equation.3 ( EMBED Equation.3 1( EMBED Equation.3 (10SecUndef.(12( EMBED Equation.3 ( EMBED Equation.3 ( EMBED Equation.3  EMBED Equation.3 Undef.Csc1Undef.( EMBED Equation.3 2( EMBED Equation.3 2( EMBED Equation.3 (1 6.2 MORE TRIG FUNCTIONS Identifying in which quadrant the angle lies is  essential for having the correct signs of the trig functions. If given, Sin  =  EMBED Equation.DSMT4  and if told that EMBED Equation.DSMT4, can we find the cos ?     1. Find cos( if sin( = 2/3 and EMBED Equation.DSMT4 2. Find tan( if sin( = 3/7 and EMBED Equation.DSMT4 3. Find csc( if cos( = EMBED Equation.DSMT4 and EMBED Equation.DSMT4 4. Find sec( if sin( = -1/3 and EMBED Equation.DSMT4 5. If Tan ( =  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4 , find all the remaining functions of (. 6. Find the values of the six trig. functions of (, if ( is an angle in standard position with the point (-5, -12) on its terminal ray. Algebra 3 Assignment # 4 (1) Sin( EMBED Equation.3 ) =  EMBED Equation.3  ,  EMBED Equation.3  . Find the remaining 5 trig. functions of  EMBED Equation.3 . (2) Cos( EMBED Equation.3 ) =  EMBED Equation.3  ,  EMBED Equation.3 . Find the remaining 5 trig. functions of  EMBED Equation.3 . (3) Tan( EMBED Equation.3 ) =  EMBED Equation.3  ,  EMBED Equation.3  . Find the remaining 5 trig. functions of  EMBED Equation.3 . (4) Sec( EMBED Equation.3 ) =  EMBED Equation.3  ,  EMBED Equation.3 . Find the remaining 5 trig. functions of  EMBED Equation.3 . (5) Csc( EMBED Equation.3 ) =  EMBED Equation.3  ,  EMBED Equation.3 . Find the remaining 5 trig. functions of  EMBED Equation.3 . (6) Cot( EMBED Equation.3 ) =  EMBED Equation.3  ,  EMBED Equation.3 . Find the remaining 5 trig. functions of  EMBED Equation.3 . (7) Sin( EMBED Equation.3 ) =  EMBED Equation.3  ,  EMBED Equation.3 . Find the remaining 5 trig. functions of  EMBED Equation.3 . (8) Find the values of the six trig. functions of (, if ( is an angle in standard position with the point (4 , (3) on its terminal ray (9) Find the values of the six trig. functions of (, if ( is an angle in standard position with the point ((5 , 12) on its terminal ray Trig Assignment #4 Answers (1) cos( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) =  EMBED Equation.3  , cot( EMBED Equation.3 ) =  EMBED Equation.3  , sec( EMBED Equation.3 ) =  EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  (2) sin( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) = ( EMBED Equation.3  , cot( EMBED Equation.3 ) = ( EMBED Equation.3  , sec( EMBED Equation.3 ) = ( EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  (3) sin( EMBED Equation.3 ) =  EMBED Equation.3  , cos( EMBED Equation.3 ) =  EMBED Equation.3  , cot( EMBED Equation.3 ) =  EMBED Equation.3  , sec( EMBED Equation.3 ) =  EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  (4) sin( EMBED Equation.3 ) =  EMBED Equation.3  , cos( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) =  EMBED Equation.3  , cot( EMBED Equation.3 ) =  EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  (5) sin( EMBED Equation.3 ) =  EMBED Equation.3  , cos( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) =  EMBED Equation.3  , cot( EMBED Equation.3 ) =  EMBED Equation.3  , sec( EMBED Equation.3 ) =  EMBED Equation.3  (6) sin( EMBED Equation.3 ) =  EMBED Equation.3  , cos( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) =  EMBED Equation.3  , sec( EMBED Equation.3 ) =  EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  (7) cos( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) =  EMBED Equation.3 , cot( EMBED Equation.3 ) =  EMBED Equation.3  , sec( EMBED Equation.3 ) =  EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  (8) sin( EMBED Equation.3 ) =  EMBED Equation.DSMT4  cos( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) =  EMBED Equation.3  , cot( EMBED Equation.3 ) =  EMBED Equation.3  , sec( EMBED Equation.3 ) =  EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  (9)sin( EMBED Equation.3 ) =  EMBED Equation.DSMT4  cos( EMBED Equation.3 ) =  EMBED Equation.3  , tan( EMBED Equation.3 ) =  EMBED Equation.3  , cot( EMBED Equation.3 ) =  EMBED Equation.3  , sec( EMBED Equation.3 ) =  EMBED Equation.3  , csc( EMBED Equation.3 ) =  EMBED Equation.3  Algebra 3 Review Worksheet (1) Complete the following table please. Rad. EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Deg.135(330((150((750(240(sincostancotseccsc (2) Sin(x) =  EMBED Equation.3  ,  EMBED Equation.3 . Find the remaining 5 trig functions of x. (3) Tan(() =  EMBED Equation.3  ,  EMBED Equation.3 . Find the remaining 5 trig functions of (. (4) Cot(x) = 0.8 ,  EMBED Equation.3 . Find the remaining 5 trig functions of x. (5) Sec(() = (3 ,  EMBED Equation.3 . Find the remaining 5 trig functions of (. (6) Find the values of the six trig. functions of (, if ( is an angle in standard position with the point ((5 , 3) on its terminal ray. Algebra 3 Review Answers (1) Rad. EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 Deg.120(135(270(330((540((150(600((750((405(240((45(sin EMBED Equation.3  EMBED Equation.3 (1 EMBED Equation.3 0 EMBED Equation.3 ( EMBED Equation.3  EMBED Equation.3 ( EMBED Equation.3 ( EMBED Equation.3 ( EMBED Equation.3 cos EMBED Equation.3 ( EMBED Equation.3 0 EMBED Equation.3 (1( EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 tan EMBED Equation.3 (1Undef( EMBED Equation.3 0 EMBED Equation.3  EMBED Equation.3 - EMBED Equation.3 (1 EMBED Equation.3 (1cot( EMBED Equation.3 (10 EMBED Equation.3 Undef EMBED Equation.3  EMBED Equation.3  EMBED Equation.3 (1 EMBED Equation.3 (1sec(2( EMBED Equation.3 Undef EMBED Equation.3 (1( EMBED Equation.3 (2 EMBED Equation.3  EMBED Equation.3 (2 EMBED Equation.3 csc EMBED Equation.3  EMBED Equation.3 (1(2Undef(2( EMBED Equation.3 (2( EMBED Equation.3 ( EMBED Equation.3 ( EMBED Equation.3  (2) cos(x) =  EMBED Equation.3  , tan(x) =  EMBED Equation.3  , cot(x) =  EMBED Equation.3  , sec(x) =  EMBED Equation.3  , csc(x) =  EMBED Equation.3  (3) sin(() =  EMBED Equation.3  , cos(() =  EMBED Equation.3  , cot(() = 2 , sec(() =  EMBED Equation.3  , csc(() =  EMBED Equation.3  (4) sin(x) = EMBED Equation.3  , cos(x) =  EMBED Equation.3  , tan(x) =  EMBED Equation.3  , sec(x) =  EMBED Equation.3  , csc(x) =  EMBED Equation.3  (5) sin(() =  EMBED Equation.3 , cos(() =  EMBED Equation.3  , tan(() =  EMBED Equation.3  , cot(() =  EMBED Equation.3  , csc(() =  EMBED Equation.3  (6) sin(() =  EMBED Equation.3 , cos(() =  EMBED Equation.3 , tan(() =  EMBED Equation.3  , cot(() =  EMBED Equation.3 , sec(() =  EMBED Equation.3  , csc(() =  EMBED Equation.3  ADDITION AND SUBTRACTION FORMULAS  sin  EMBED Equation.DSMT4  = sin EMBED Equation.DSMT4 cos  EMBED Equation.DSMT4  + cos  EMBED Equation.DSMT4 sin EMBED Equation.DSMT4  sin  EMBED Equation.DSMT4  = sin  EMBED Equation.DSMT4 cos EMBED Equation.DSMT4  - cos EMBED Equation.DSMT4 sin EMBED Equation.DSMT4  cos  EMBED Equation.DSMT4  = cos EMBED Equation.DSMT4 cos EMBED Equation.DSMT4  - sin EMBED Equation.DSMT4  sin EMBED Equation.DSMT4  cos  EMBED Equation.DSMT4  = cos EMBED Equation.DSMT4 cos EMBED Equation.DSMT4  + sin EMBED Equation.DSMT4 sin EMBED Equation.DSMT4  tan  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  tan  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4   SPECIAL ANGLES  EMBED Equation.DSMT4  2nd 3rd 4th 120 ___ ___ 135 ___ ___ 150 ___ ___ 180 ___ ___  COMBINATIONS 15 EMBED Equation.DSMT4  = 345 EMBED Equation.DSMT4  = 255 EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  = EXAMPLES Evaluate each expression 1) sin 75 EMBED Equation.DSMT4  sin (45 + 30) sin(120 45) 2) cos 345 EMBED Equation.DSMT4  3) tan  EMBED Equation.DSMT4  Simplify the following: 4) cos (270 EMBED Equation.DSMT4  - x) 5) sin ( x +  EMBED Equation.DSMT4 ) = 6) cos (  EMBED Equation.DSMT4  ) Find each of the following numbers: If sin A =  EMBED Equation.DSMT4  , 0 < A <  EMBED Equation.DSMT4  and cos B =  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  7) sin (A + B) 8) cos (A B) 9) tan (A + B ) Algebra 3 Trig Formulas Assignment #6 (1) Find each of the following numbers please. (a) sin(15 EMBED Equation.3 ) (b) cos(15 EMBED Equation.3 ) (c) sin(105 EMBED Equation.3 ) (d) cos(75 EMBED Equation.3 ) (e) sin EMBED Equation.DSMT4  (f) cos EMBED Equation.DSMT4  (g) sin(345 EMBED Equation.3 ) (h) tan(15 EMBED Equation.3 ) (2) Simplify each of the following please. (a) sin(90 EMBED Equation.3 + x) (b) cos( EMBED Equation.DSMT4 ( x) (c) sin(180 EMBED Equation.3 ( x) (d) cos( EMBED Equation.DSMT4 + x) (3) Sin(A) =  EMBED Equation.3  , A is in Quadrant I, Cos(B) =  EMBED Equation.DSMT4  EMBED Equation.3  , B is in Quadrant II. Find each of the following numbers please. (a) sin(A + B) (b) cos(A + B) (c) sin(A ( B) (d) cos(A ( B) (e) tan(A + B) (f) csc(A ( B) Assignment #6 Answers (1) (a)  EMBED Equation.3  (b)  EMBED Equation.3  (c)  EMBED Equation.3  (d)  EMBED Equation.3  (e)  EMBED Equation.3  (f)  EMBED Equation.3  (g)  EMBED Equation.3  (h)  EMBED Equation.3  (2) (a) cos EMBED Equation.3  (b) sin EMBED Equation.3  (c) sin EMBED Equation.3  (d) (cos EMBED Equation.3  (3) (a)  EMBED Equation.3  (b)  EMBED Equation.3  (c)  EMBED Equation.3  (d)  EMBED Equation.3  (e)  EMBED Equation.3  (f)  EMBED Equation.3  DOUBLE AND HALF ANGLE FORMULAS Double Angle Formulas Half Angle Formulas  EMBED Equation.DSMT4   EMBED Equation.DSMT4  Find each of the following numbers, please. 1) sin (  EMBED Equation.DSMT4 ) 2) cos ( EMBED Equation.DSMT4 ) If Sin A =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  EMBED Equation.DSMT4  Tan B =  EMBED Equation.DSMT4  Find the following numbers, please. 3) sin ( EMBED Equation.DSMT4 A) 4) cos (2B) 5) sin (A + B) Algebra 3 Double and Half Angle Formulas Assignment #7 (1) Find each of the following numbers please. (a) sin(67 EMBED Equation.3  EMBED Equation.3 ) (b) cos EMBED Equation.DSMT4  (c) sin EMBED Equation.DSMT4  (d) cos(202 EMBED Equation.3  EMBED Equation.3 ) (2) Sin(A) =  EMBED Equation.3  ,  EMBED Equation.DSMT4 , Tan(B) =  EMBED Equation.3  ,  EMBED Equation.DSMT4 . Find each of the following numbers please. (a) sin( EMBED Equation.3 A) (b) cos( EMBED Equation.3 A) (c) sin( EMBED Equation.3 B) (d) sec( EMBED Equation.3 B) (e) sin(2B) (f) cos(2A) (g) csc(A ( B) (h) cos(A + B) Answers (1) (a)  EMBED Equation.3  (b)  EMBED Equation.3  (c)  EMBED Equation.3  (d) ( EMBED Equation.3  (2) (a)  EMBED Equation.3  (b)  EMBED Equation.3  (c)  EMBED Equation.3  (d)  EMBED Equation.3  (e)  EMBED Equation.3  (f)  EMBED Equation.3  (g)  EMBED Equation.3  (h)  EMBED Equation.3  Algebra 3 Formula Review Worksheet, Assignment #8 (1) Find each of the following numbers please. (a) sin(15 EMBED Equation.3 ) (b) cos(105 EMBED Equation.3 ) (c) sin(195 EMBED Equation.3 ) (d) cos(285 EMBED Equation.3 ) (e) sin(112 EMBED Equation.3  EMBED Equation.3 ) (f) cos EMBED Equation.DSMT4  (g) tan(75() (h) sec EMBED Equation.DSMT4  (2) Simplify each of the following please. (a) sin(180 EMBED Equation.3 + x) (b) cos( EMBED Equation.DSMT4 + x) (c) sin( EMBED Equation.DSMT4 ( x) (d) cos(180 EMBED Equation.3 ( x) (3) Sin(A) = ( EMBED Equation.3  ,  EMBED Equation.DSMT4 , Sec(B) =  EMBED Equation.3  ,  EMBED Equation.DSMT4 . Find each of the following numbers. (a) sin(A + B) (b) cos(A + B) (c) sin(A ( B) (d) cos(A ( B) (e) sin(2B) (f) cos(2A) (g) sin EMBED Equation.3  (h) cos EMBED Equation.3  Answers (1) (a)  EMBED Equation.3  or  EMBED Equation.3  (b)  EMBED Equation.3  or ( EMBED Equation.3  (c)  EMBED Equation.3  or ( EMBED Equation.3  (d)  EMBED Equation.3  or  EMBED Equation.3  (e)  EMBED Equation.3  (f)  EMBED Equation.3  (g)  EMBED Equation.3  (h)  EMBED Equation.3  (2) (a) (sin EMBED Equation.3  (b) sin EMBED Equation.3  (c) (cos EMBED Equation.3  (d) (cos EMBED Equation.3  (3) (a)  EMBED Equation.3  (b)  EMBED Equation.3  (c)  EMBED Equation.3  (d) DEK\]z  . / C F O R c d  Ͽvh8CJOJQJaJhqCJOJQJaJ" j-h=h8qCJOJQJaJh=h8qCJOJQJaJh=h8q5CJOJQJaJh=hp5CJOJQJaJhp5CJOJQJaJ"h5h55>*CJ OJQJaJ "hh8q5>*CJ$OJQJaJ$+EFz A M }  ;    / ; gdo|dgd:y"dgdq  !dgd8qdgd8q$a$gd8q<<e   $ % & ' ; > ? 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FMathType 4.0 Equation MathType EFEquation.DSMT49qEquation Native q_1074668625Fu'$u'$Ole uCompObjviObjInfoxEquation Native y_1074670109NFu'$u'$Ole }@6M6GlxDSMT4WinAllBasicCodePagesTimes New RomanSymbolMT Extra!O!/!"O!/G_APAPAE%B_AC_AH*_HA@BHA*_D_E_E_A  780 "o FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObj~iObjInfoEquation Native _1074669115Fu'$u'$@6M6GlxDSMT4WinAllBasicCodePagesTimes New RomanSymbolMT Extra!O!/!"O!/G_APAPAE%B_AC_AH*_HA@BHA*_D_E_E_A  495 "oP FMathType 4.0 Equation MathType EFEquation.DSMT49q|Ole CompObjiObjInfoEquation Native @6M6GlxDSMT4WinAllBasicCodePagesTimes New RomanSymbolMT Extra!O!/!"O!/G_APAPAE%B_AC_AH*_HA@BHA*_D_E_E_A  90 "o FMathType 4.0 Equation MathType EFEquation.DSMT49q_1074669455Fu'$u'$Ole CompObjiObjInfo@6M6GlxDSMT4WinAllBasicCodePagesTimes New RomanSymbolMT Extra!O!/!"O!/G_APAPAE%B_AC_AH*_HA@BHA*_D_E_E_A   12 FMathType 4.0 Equation MathType EFEquation.DSMT49qEquation Native _1074669684IFu'$u'$Ole CompObjiObjInfoEquation Native _1074669530DFu'$u'$Ole @6M6GlxDSMT4WinAllBasicCodePagesTimes New RomanSymbolMT Extra!O!/!"O!/G_APAPAE%B_AC_AH*_HA@BHA*_D_E_E_A    2  2 FMathType 4.0 Equation MathType EFEquation.DSMT49qCompObjiObjInfoEquation Native _10746696750Fu'$u'$@6M6GlxDSMT4WinAllBasicCodePagesTimes New RomanSymbolMT Extra!O!/!"O!/G_APAPAE%B_AC_AH*_HA@BHA*_D_E_E_A    3  2 FMathType 4.0 Equation MathType EFEquation.DSMT49qOle CompObjiObjInfoEquation Native @6M6GlxDSMT4WinAllBasicCodePagesTimes New RomanSymbolMT Extra!O!/!"O!/G_APAPAE%B_AC_AH*_HA@BHA*_D_E_E_A    2  2dD0_1107328880Fu'$u'$Ole PIC dMETA     .  & Timesw@ +CwCw w0-!cscPSymbolw@ =CwCw w0-!p Timesw@ ,CwCw w0-!4-   & 'PICT 2CompObjhObjInfoOlePres0002dxpr  " currentpoint ",Times +csc, Symbol( p+4" S/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 928 div 896 3 -1 roll exch div scale currentpoint translate 64 42 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 532 403 moveto 280 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (csc) -9 502 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) 540 261 sh 384 /Times-Roman f1 (4) 580 795 sh end MTsave restore d-MATH! cscp4du FMathType 4.0 Equation Equation.2Equation.DSMT49q    .  & Timesw@ +CwCw w0-!cscPSymbolw@ =CwCw w0-!p Timesw@ ,CwCw w0-!4-   & '! cscp4dD0Equation Native =_1107328881Fu'$u'$Ole PIC dMETA PICT 8CompObjhObjInfo    .  & Timesw@Z CwCw w0-!cotPSymbolw@ -CwCw w0-!p Timesw@Z CwCw w0-!6-   & '8dxpr  " currentpoint ",Times +cot, Symbol( p+6" Y/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 928 div 896 3 -1 roll exch div scale currentpoint translate 64 -985 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 524 1430 moveto 280 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (cot) -9 1529 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) 532 1288 sh 384 /Times-Roman f1 (6) 568 1822 sh end MTsave restore d-MATH! cotp6du FMathType 4.0 Equation Equation.2Equation.DSMT49q    .  & Timesw@Z CwCw w0-!cotOlePres000Equation Native =_1107328882Fu'$u'$Ole PSymbolw@ -CwCw w0-!p Timesw@Z CwCw w0-!6-   & '! cotp6di>PIC dMETA PPICT CompObjh     !#$%&'()+,-./0123456789:;=@ABCDEFJLMNOPQRTUVWXYZ[\]^_`abcdfijklmnosuvwxyz{|}~i>    ! .  & Timesw@ CwCw w0-!sec !2 PSymbolw@ CwCw w0-!p  & ' !dxpr  !" ! currentpoint ",Times + sec)2, Symbol)p/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1056 div 384 3 -1 roll exch div scale currentpoint translate 64 -1544 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (sec) -19 1864 sh 384 /Times-Roman f1 (2) 511 1864 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) 699 1864 sh end MTsave restore d$MATH sec2pbl FMathType 4.0 Equation Equation.2Equation.DSMT49qObjInfoOlePres000pEquation Native 4_1107328883Fu'$u'$H    ! .  & Timesw@ CwCw w0-!sec !2 PSymbolw@ CwCw w0-!p  & ' sec2pOle PIC  dMETA "PICT *Td0   " .  & Timesw@X OCwCw w0-!sec!3 PSymbolw@ CwCw w0-!p Timesw@X PCwCw w0-!2-   & 'T"dxpr  """ currentpoint ",Times +sec( 3, Symbol)p(2"  l/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1088 div 896 3 -1 roll exch div scale currentpoint translate 64 -2137 translate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 522 2582 moveto 459 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (sec) -19 2681 sh 384 /Times-Roman f1 (3) 538 2440 sh (2) 655 2974 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) 709 2440 sh end MTsave restore d0MATH$ sec3p2 e FMathType 4.0 Equation Equation.2Equation.DSMT49q  CompObj<hObjInfo>OlePres000?Equation Native G@ " .  & Timesw@X OCwCw w0-!sec!3 PSymbolw@ CwCw w0-!p Timesw@X PCwCw w0-!2-   & '$ sec3p2_1107328884Fu'$u'$Ole HPIC IdMETA Kd0   # .  & Timesw@a VCwCw w0-!tan!4 PSymbolw@ :CwCw w0-!p Timesw@a WCwCw w0-!3-  & 'O#dxpr  #"# currentpoint ",Times +tan( 4, Symbol)p(3" g/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 1120 div 896 3 -1 roll exch div scale currentpoint translate 64 -534 tranPICT SOCompObjehObjInfogOlePres000hslate /thick 0 def /th { dup setlinewidth /thick exch def } def 16 th 524 979 moveto 487 0 rlineto stroke /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /Times-Roman f1 (tan) -4 1078 sh 384 /Times-Roman f1 (4) 552 837 sh (3) 677 1371 sh /f2 {ff matrix dup 2 .22 put makefont dup /cf exch def sf} def 384 /Symbol f2 (p) 739 837 sh end MTsave restore d0MATH$ tan4p3nc FMathType 4.0 Equation Equation.2Equation.DSMT49q   # .  & Timesw@a VCwCw w0-!tan!4 PSymbolw@ :CwCw w0-!p Timesw@a WCwCw w0-!3-  & 'Equation Native p@_1107328885Fu'$u'$Ole qPIC rd$ tan4p3dX I  / .  & Timesw@| CwCw w0-!cotPSymbolw@ 9CwCw wMETA tPICT CompObjhObjInfo0-!-PSymbolw@| CwCw w0-!p Timesw@ :CwCw w0-!4 -'PSymbolw@| CwCw w0-! 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