Trigonometric functions of any angle

    • [PDF File]TRIGONOMETRIC FUNCTIONS OF ANY ANGLE

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      TRIGONOMETRIC FUNCTIONS OF ANY ANGLE •If the angle is a quadrantalangle, draw the angle, pick a point on its terminal side, and apply the definition of the trigonometric functions. •If the angle lies in a quadrant: 1.Find the reference angle of . 2.Find the value of the trigonometric function at . 3.Adjust the sign (+ or −) of the value ...

    • [PDF File]9.3 Trigonometric Functions of Any Angle

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      Trigonometric Functions of Any Angle You can generalize the right-triangle defi nitions of trigonometric functions so that they apply to any angle in standard position. Evaluating Trigonometric Functions Given a Point Let (−4, 3) be a point on the terminal side of an angle θ in standard position. Evaluate the six trigonometric functions of θ.

    • [PDF File]r x y z 22 - UTEP

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      Evaluating Trigonometric Functions of Any Angle – To find the value of a trigonometric function of any angle θ: 1. Determine the function value for the associated reference angle θ’. 2. Depending on the quadrant in which θ lies, affix the appropriate sign to the function value. Examples: Find two solutions of the equation.

    • [PDF File]4.4 Trigonometric Functions of Any Angle

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      Evaluating Trigonometric Functions of Any Angle To find the value of a trigonometric function of any angle 1. Determine the function value for the associated reference angle 2. Depending on the quadrant in which lies, affix the appropriate sign to the function value..: (degrees) (radians) 0 010 100 013 3 Undef. 0 Undef. 3 tan 1 1 2 2 2 3 2 cos ...

    • [PDF File]Trig Ratios of Any Angle Date Period

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      Use the given point on the terminal side of angle to find the value of the trigonometric function indicated. 15) sin x y ( , ) 16) cot x y ( , ) 17) sec x y ( , ) 18) sin x y ( , ) Find the exact values of the five trigonometric ratios not given. 19) cot and sin 20) cos and sin

    • [PDF File]2. TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES lies in ...

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      10 r ( x, y) θ O y x . Definition 2.1: Trigonometric Functions of a General Angle Let θ be an angle in standard position and suppose that ( x , y ) is any point other than ( 0 , 0 ) on the terminal side of θ(Figure 2.3).If r = x2 +y2 is the distance between ( x, y ) and ( 0 , 0 ), then the six trigonometric functions of θ are defined by Using similar triangles, you can see that the values ...

    • [PDF File]Trigonometric Functions - CPP

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      Trigonometric functions of any angle θ' in terms of angle θ in quadrant I Trigonometric functions of negative angles Some useful relationships among trigonometric functions Double angle formulas Half angle formulas Angle addition formulas Sum, difference and product of trigonometric functions

    • [PDF File]Section 5.3: Trigonometric Functions of Any Angle

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      Goal: To find the values of the 6 trig functions of any angle (not just acute) Ex.Find the six trig functions of the angle determined by... Section 5.3: Trigonometric Functions of Any Angle Monday, August 25, 2014 1:54 PM

    • [PDF File]13.3 Trigonometric Functions of Any Angle

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      Page 1 of 2 13.3 Trigonometric Functions of Any Angle 785 If the terminal side of † lies on an axis, then † is a The diagrams below show the values of x and y for the quadrantal angles 0°, 90°, 180°, and 270°. Trigonometric Functions of a Quadrantal Angle Evaluate the six trigonometric functions of † = 180°. SOLUTION When † = 180°, x = ºr and y = 0.

    • [PDF File]Trigonometric Functions of Any Angle - Alamo

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      Trigonometric Functions of Any Angle . This section develops the trigonometric functions based on angle measurement and relates it to the concept of the circular or wrapping function developed previously, which relied on movement around the perimeter of a unit circle.

    • [PDF File]8.3 Trigonometric Functions of Any Angle

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      Trigonometric Functions of Any Angle You can generalize the right-triangle defi nitions of trigonometric functions so that they apply to any angle in standard position. Evaluating Trigonometric Functions Given a Point Let (−4, 3) be a point on the terminal side of an angle θ in standard position. Evaluate the six trigonometric functions of θ.

    • [PDF File]Section 4.4 Trigonometric Functions of Any Angle 537

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      Defi nitions of Trigonometric Functions of Any Angle Let u be any angle in standard position and let P = (x, y) be a point on the terminal side of u. If r = 2x2 + y2 is the distance from (0, 0) to (x, yas ), shown in Figure 4.41 on the previous page, the six trigonometric functions of U are

    • [PDF File]12 Trigonometric Functions of Any Angle

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      tions of any angle, not just acute angles, (2) the sign of the trigonometric functions in each quadrant of the coordinate plane, and (3) the use of refer-ence angles which reduce the question of nding the trigonometric functions of an angle to that of nding the trigonometric functions of the special an-gles 30 ;45 ;and 60 : Let be an angle in ...

    • [PDF File]CHAPTER 3 Trigonometric Functions

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      The Trigonometric Functions 33 The unit circle is the circle of radius 1 that is centered at the origin. It is the graph of the equation x 2+ y =1.That is, it is the set of all points ( x, y) on the plane for which 2+ = 1. To see why this is so, take any point (x,y) on the circle.

    • [PDF File]Section Trigonometric Functions of Any Angle Objectives

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      Definitions of Trigonometric Functions of Any Angle Let be any angle in standard position and let be a point on the terminal side of If is the distance from (0,0) to as shown in Figure 4.41,the six trigonometric functions of are defined by the following ratios: y r sin u= x r cos u= y x tan u= , x 0 x y cot u= , y 0. r x sec u= , x 0 r y csc u ...

    • [PDF File]Ch 6.3: Trigonometric functions of any angle

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      Ch 6.3: Trigonometric functions of any angle In this section, we will 1.extend the domains of the trig functions (as well as the need for it) using the unit circle 2.look at some properties of the unit circle 3.evaluate trig. values using reference angles 4.investigate the relationships between trig. functions

    • [PDF File]Chapter 1. Functions 1.3. Trigonometric Functions

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      1.3 Trigonometric Functions 3 Definition. We define the six trigonometric functions for any angle θ by first placing the angle in standard position in a circle of radius r. Then define the trigonometric functions in terms of the coordinates of the point P(x,y) where the angle’s terminal ray intersects the circle as follows: sinθ = y r ...

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