7.4Trigonometric Functions of General Angles F10

# 7.4Trigonometric Functions of General Angles F10 - 7.4...

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1 7.4 Trigonometric Functions of General Angles In this section, we will study the following topics: Evaluating trig functions of any angle Using the unit circle to evaluate the trig functions of quadrantal angles Finding coterminal angles Using reference angles to evaluate trig functions.

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2 In 7.3, we looked at the definitions of the trig functions of acute angles of a right triangle. In this section, we will expand upon those definitions to include ANY angle. We will be studying angles that are greater than 90° and less than 0°, so we will need to consider the signs of the trig functions in each of the quadrants. We will start by looking at the definitions of the trig functions of any angle. Trig Functions of Any Angle
3 Definitions of Trigonometric Functions of Any Angle Let θ be an angle in standard position with ( x, y ) a point on the terminal side of θ and Definitions of Trig Functions of Any Angle 2 2 r x y = + sin csc cos sec tan cot y r r y x r r x y x x y θ = = = = = = y x θ ( x, y ) r

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4 Let (-12, -5) be a point on the terminal side of θ . Find the exact values of the six trig functions of θ . Example x -5 y ( -12, -5 ) -12 First you must find the value of r: 2 2 r x y = +
5 Let (-3, 7) be a point on the terminal side of θ . Find the exact values of the six trig functions of θ . You Try!

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6 Since the radius is always positive (r > 0), the signs of the trig functions are dependent upon the signs of x and y . Therefore, we can determine the sign of the functions by knowing the quadrant in which the terminal side of the angle lies.
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## This note was uploaded on 01/12/2011 for the course MAT117 MAT 117 taught by Professor Ranjitrebello during the Spring '09 term at University of Phoenix.

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7.4Trigonometric Functions of General Angles F10 - 7.4...

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