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Pre-Calc Book Section 5.2 Trigonometric Functions of Real Numbers Objectives: • How do you find the value of any given trig angle? • How can understanding the signs of the quadrants help in finding the function value of any trig angle? Trigonometric Functions of Any Angle y sin r x cos r y tan , x 0 x r csc , y 0 y r sec , x 0 x x cot , y 0 y Ex. 1 Find the six trig functions of each given real number t. a) t 6 b) t 2 1 3 , 2 2 Ex.2 Let be a point on the terminal side of . Find the sine, cosine, and tangent of . Ex.3 Let (-3,4) be a point on the terminal side of . Find the sine, cosine, and tangent of . Signs of Trig Functions , , , , Quad I II III IV Positive All Trig. Functions Sine/Cosecant Tangent/Cotangent Cosine/Secant All Students Take Calculus Ex. 4 Determine the sign of the following trig functions. a) cos > 0, because the terminal point of t is in Quad I 3 3 b) tan 4 c) > 0, because the terminal point of t 4 is in Quad III 7 7 < 0, because the terminal point of t sin 4 4 is in Quad IV Class Work Find the six trig functions of each given real number t. 1. t 4 2. t 3 Determine the sign of the following trig functions. 3. 5 tan 6 4. cos 7 5. csc 5 4 Ex 5. Evaluate the sine, cosine and tangent of the given angle. a ) 570 b) 60 13 c) 4 11 d) 3 Ex. 6 Find the exact value of the trig function at the given real number t. 2 a) cos 3 b) tan 3 c) 19 sin 4 d) 2 cos 3 e) 5 sin 3 f) 5 tan 6 Class Work Find the exact value of the trig function at the given real number t. 6. 5 sin 6 7. 4 tan 3 8. 14 cos 3 Ex.7 State the quadrant in which lies. a) cos 0, sin 0 b) sec 0, tan 0 c) sin 0, cot 0 Fundamental Identites Ex 8. If 3 cos t 5 and t is in quadrant IV, find the values of all the trig functions at t. Ex 9. Find the values of the six trig functions of in the given quadrant. 5 a) tan 4 cos 0 b) csc 3 tan 0 2 c) sin 7 cot 0 Class Work Find the values of all the trig functions of t from the given information. 13. 4 cos t 5 14. 1 tan t 4 In quad III In quad III 15. sec t 2 sint < 0 HW #3 p.416 3-19 eoo, 27-35 eoo, 63-69 odd