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Some Trigonometric Identities. Negative Angle Identities sin(- ) = - sinθ cos(- ) = cosθ tan(- ) = - tanθ csc(- ) = - cscθ sec(- ) = secθ cot(- ) = - cotθ Addition and Subtraction Identities sin (A + B) = sin A cos B + cos A sin B cos (A + B) = cos A cos B – sin A sin B sin (A – B) = sin A cos B – cos A sin B cos (A – B) = cos A cos B + sin A sin B Co-function Identities If A + B = π2 sin A = cos B sec A = csc B tan A = cot B Quotient Identities 1 sin 1 secθ = cos cscθ = tanθ = cotθ = 1 tan = Pythagorean Identities 2 2 sin θ + cos θ = 1 Double Angle Identities sin 2 θ = 2sinθ cosθ cos 2θ = cos θ -- sin 2 sin 2 2 Half-Angle Identities = 2cos θ -- 1 cos tan 2 2 2 = ± 1 – cos 2 = ± 1 + cos 2 = ± 1 – cos 1 + cos = 1 – 2sin2θ 7/02 UT Learning Center, JES A332A, 512-471-3614 cos sin THE UNIT CIRCLE (0,1) ( , 1 2 ( , 2 2 ( , ) 1 2 3 2 2 2 ) 3 2 3 4 2 ) 2 3 1 2 ( , 3 3 2 ) 2 2 4 5 6 ( , ) 3 2 6 3 2 1 2 1 2 0 (1,0) (- 1,0) ( , 2 2 ( , ) ) 7 6 ( , ) 2 2 2 2 11 6 5 4 7 4 4 3 ( , 1 2 3 2 ) 5 3 ( , 1 2 3 2 3 2 ( , ) 3 2 1 2 ( , ) 2 2 2 2 ) (0,- 1) sin TRIGONOMETRIC DEFINITIONS SPECIAL ANGLE TRIANGLES y opposite r hypotenuse 2 x adjacent cos r hypotenuse tan y opposite x adjacent 7/02 1 30° 1 3 or if it is the unit circle, r=1 so 45° 60° 1 2 2 1 2 30° 45° y 60° 2 1 45° 1 r 45° 2 2 x UT Learning Center, JES A332A, 512-471-3614 3 2