TRIGONOMETRIC IDENTITIES Reciprocal Identities Tangent & Cotangent Identities Pythagorean Identities

Cofunction Identities ( is the complement of ) Negative Identity Functions

Ex. Solve for values between 0˚ & 90˚ 1. If tan Ø=2, find cot Ø. 2. If tan Ø=7/2 , find sin Ø. Recall: tan = O/A r 7 2 Use Pythagorean Theorem to find r (hypotenuse):

Ex. Express each value as a function of an angle in Quadrant I. 1. sin 458˚ sin 458˚= sin 82˚ 458˚=360˚+98˚ 98˚ is an 82˚ in Quad. II 98˚ 458˚ 82˚ Back in the day before there was a plethera of calculators, books had trig tables that listed the sin, cos, & tan for angles between 0˚ & 90˚ (in Quad. I)…these were ‘reference angles’ for the rest of the angles. Therefore, 82˚ is a reference angle.

Ex. Simplify. 1. Recall:

Ex. Simplify. 2. Recall: (…find LCD which is cos x) (…since sin2x + cos2x=1) (…since sec x is reciprocal of cos x)