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1.4 - Trigonometric Functions of Any Angle

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2 Objectives Evaluate trigonometric functions of any angle. Use reference angles to evaluate trig functions. Use trig identities to evaluate trig functions Use trig models to solve real world problems

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3 Definitions of trigonometric functions Syr Cxr Tyx

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Examples: 1) Let (-4, -3) be a point on the terminal side of . Evaluate the six trigonometric functions of . 2) Let (-5, 12) be a point on the terminal side of . Evaluate the six trigonometric functions.

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Example: Use the given point on the terminal side of an angle in standard position. Evaluate the six trigonometric functions of . 1) (4, 5) 2)

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6 Quadrant angles cos sin 0 /2 3/2 22 xy

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Quadrantal Angles Quadrantal angles- angles whose terminal side of lies on an axis.

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Quadrantal Angles (Continue)

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Examples: 1) Evaluate the six trigonometric functions of = 270. 2) Evaluate the six trigonometric functions of = 90.

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10 Trigonometric function signs A ll S tudents T ake C alculus Sin/csc Tan/cotCos/sec All 6 trig functions are positive in quadrant 1

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11 Find the quadrant 1. sin > 0; cos