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Algebra 2 13.3A Trigonometric Functions of General Angles Obj: able to find values of trigonometric functions for general angles; able to use reference triangles Evaluating Trigonometric Functions Let θ (Theta) be an angle in standard position with any point (x, y) (except the origin) on the terminal side of θ. Let r = y (x, y) x +y . 2 2 y y x tan θ = , x ≠ 0 cosθ = r x r r x r csc θ = , y ≠ 0 cot θ = , y ≠ 0 sec θ = , x ≠ 0 y y x Remember: (x, y) can have positive or negative values. For acute angles, the definitions above give the same values as those given by the definitions in Lesson 13.1 sin θ = r y θ x x Initial side r = x2 + y 2 The Reference Angle of an Angle Let θ be an angle in standard position. Its Reference Angle is the acute angle θ ' (read theta prime) formed by the terminal side of θ and the x-axis. (x, y) Quadrant IV Quadrant III Quadrant II y y y θ θ θ Initial side x x θ‘ θ‘ Initial side θ‘ Initial side (x, y) (x, y) Evaluating Trigonometric Functions of Any Angle Use the following steps to evaluate a trigonometric function of any angle θ . 1. Find the reference angle θ ’. 2. Evaluate the trigonometric function for the angle θ ’. 3. Use the quadrant in which θ lies to determine the sign of the trigonometric function of Find the exact value of the six trigonometric functions of 1. (-5, 12) θ x if the terminal side of 2. ( -3, -4) θ θ. in standard position contains the point. Find the exact value of the six trigonometric functions of 3. (0, 3) I don’t get it at all 1 What do you still need to work on? I sort of get it 2 θ if the terminal side of 4. ( 5, -5) θ in standard position contains the point. Rate yourself on how well you understood this lesson. I understand I understand most of it but I it pretty well need more practice 3 4 I got it! 5