2 cos 2 x 1 0
[DOC File]CHAPTER 10 : TRIGONOMETRIC FUNCTIONS, IDENTITIES & …
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the cosine function is periodic with period 2( since cos x = cos (x + 2()-1 ( cos x ( 1, i.e. the range is [-1, 1] the curve cuts the x-axis at 0, ( , ( , ( , . . . Graph of cos x: y. x - - 0 Note: The cosine graph has the same shape as the sine graph but the former is shifted by a distance of to the left on the x-axis.
[DOCX File]Chapter 2 Inverse Trigonometric Functions
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cos -1 3 2 . Q9. If . sin -1 x =y , then what will be the range of y? Q10. Show that . sin -1 2 x 1- x 2 =2 sin -1 x . Q11. Find the value of . cos -1 cos 13 π 6 . Q12. Find the value . of . tan -1 2 11 + tan -1 7 24 . Q13. Find the value . of . tan -1 3 a 2 x- x 3 a 3 - 3 a x 2 . Q14. Express . 2 tan -1 x …
[DOC File]2 - University of Arizona
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The value of a is 0 at x = and 2k plus these values (k any integer). Theses give us the x values of the vertical. asymptotes. c) On the unit circle, etc. cos x = a. As long as we stay on the unit circle, the horizontal coordinate (a) will stay between -1 and 1, inclusive. 7. cos (2x) = cos(x+x) = (cos x)(cos x) – (sin x)(sin x) = . 8.,9.
[DOC File]Pre-Calculus Parametrics Worksheet #2
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5. x = cos t 6. x = 4 + 2 cos t. y = 2 sin2t y = -1 + 4 sin t. Problems 7 and 8: Write two new sets of parametric equations for the following rectangular equations. 7. y = (x + 2)3 – 4 8. x = 9. For the parametric equations x = t and y = t2 a) Sketch the graph and state an appropriate window. b) Graph x = t – 1 …
[DOC File]ANSWERS TO DAVID ESSNER EXAM II, 1982-93
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(a) f(x) = x(3x – 1)/(2x – 1). To make f(x) > 0 a given x must lie between 0 and 1/3 or be > 1/2 (b) Use the identity cos 2A = 2 cos2A – 1 with A = 22 1/2 . Then /2 = cos 45 = 2 cos2 22 1/2 - 1 = 2(x/2)2 - 1 where x is the length of the other side. (d) This is the intersection of the circle (x – 2)2 + y2 = 1 and the ellipse (x – 1)2…
[DOC File]6.2 TRIG FUNCTIONS -- UNIT CIRCLE
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sin t = y/1 = y csc t = 1 / y (y ( 0) cos t = x/1 = x sec t = 1 / x ( x ( 0) tan t = y / x (x ( 0) cot t = x / y (y ( 0) Note: The unit circle is just a special case of this general theorem! Example: A) Find the values of the trig functions corresponding to (-4/5, 3/5) sin θ = csc θ = ...
[DOC File]EGR 511
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-1.1518 0.7028 -1.4845 -0.14943 0.13534 Use the divided-difference table to estimate f(0.15), using a) a polynomial of degree 2 through the first three points.
[DOC File]Paper Reference(s)
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(a) Express 3 sin x + 2 cos x in the form R sin (x + α) where R > 0 and 0 < α < . (4) (b) Hence find the greatest value of (3 sin x + 2 cos x)4. (2) (c) Solve, for 0 < x < 2π, the equation 3 sin x + 2 cos x = 1, giving your answers to 3 decimal places. (5) June 2007. 7. (a) Express 4 cosec2 2θ − cosec2 θ in terms of sin θ and cos θ. (2)
[DOC File]TRIGONOMETRY
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1 0 Cot ( ( (1 0 1 Undef. Sec (2 ( Undef. ( (1 (2 Csc (2 1 2 ( Undef. ( Radian Measure Degree Measure (270( 540( (420( 150( 585( (210( 315( 270( Sin 1 0 ( ( ( (1 Cos 0 (1 ( ( ( 0 Tan Undef. 0 ( ( 1 ( (1 Undef. Cot 0 Undef. ( ( 1 ( (1 0 Sec Undef. (1 2 ( ( ( Undef. Csc 1 Undef. ( 2 ( 2 ( (1 6.2 MORE TRIG FUNCTIONS
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