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MAT 155P - PRECALCULUS MATHEMATICS PLUS Chapter 4 Formulas Radian Measure Arc Length s r s r Even Identities Odd Identities sec t sec t csc t csc t sin t sin t cos t cos t tan t tan t cot t cot t Pythagorean Identities tan2 t 1 sec2 t 1 cot2 t csc2 t Cofunction Identities tan cot 90 sec csc 90 sin cos 90o o o cot tan 90 csc sec 90 cos sin 90o o *If is in radians, replace 90o with o 2 How to Find the Coterminal Angles of a Given Angle 1. If 360 (2 ) , subtract appropriate multiples of 360 (2 ) to obtain . 2. If 0 , add appropriate multiples of 360 (2 ) to obtain . How to Find Reference Angles for Angles Less Than 360 o (2π) Quadrant Angle Reference angle α I 0˚ < < 90 α= II 90˚ < < 180 ˚ α = 180 ˚ – III 180˚ < < 270 ˚ α = – 180˚ IV 270˚ < < 360 ˚ α = 360 ˚ – If is measure in radians and 0 2 , replace 180 with π in these calculations. Page 1 of 3 How to Find Reference Angles for Angles Greater Than 360 o ( 2 ) 1. Subtract appropriate multiples of 360 , until you obtain an angle between 0 and 360 , from . 2. Find the reference angle for the result from step 1. How to Find Reference Angles for Angles Less Than -360o (- 2 ) 1. Add appropriate multiples of 360o until you obtain an angle between 0 and 360 , to . 2. Find the reference angle for the result from step 1. Steps for Evaluating Trigonometric Functions for Any Angle 1. If 360 or 0 , find a coterminal angle between 0 and 360 . Otherwise go to Step 2. 2. Find reference angle. 3. Find trigonometric function value for the reference angle. 4. Determine the sign of the trigonometric function based on the quadrant in which lies to prefix the appropriate sign of the function value in Step 3. Finding Exact Values , 1. For sin 1 x find the value of in that satisfies sin x . 2 2 2. For cos 1 x find the value of in 0, that satisfies cos x . , that satisfies tan x . 2 2 3. For tan 1 x find the value of in Cancellation Equations for Inverse Sine, Cosine, and Tangent Functions f 1 ( f ( x)) sin 1 (sin x) x where x 2 2 f ( f 1 ( x)) sin(sin 1 x) x where -1 x 1 f 1 ( f ( x)) cos 1 (cos x) x where 0 x f ( f 1 ( x)) cos(cos 1 x) x where -1 x 1 f 1 ( f ( x)) tan 1 (tan x) x where f ( f 1 ( x)) tan(tan 1 x) x where x x 2 2 Page 2 of 3 Page 3 of 3