Pre calculus Problem of the Day Homework p. 578 1-21 odds Simplify the following: 2 2 a) sin cos 6 6 2 2 b) sin cos 4 4 4 2 4 2 c) sin cos 3 3 Trigonometric Identities - a statement of equality that is true for all values where the function is defined. Reciprocal Identities: 1 sin csc 1 cos sec 1 tan cot 1 csc sin 1 sec cos 1 cot tan Quotient Identities: sin tan cos cos cot sin Pythagorean Identities: Even/Odd Identities: sin 2 cos2 1 sin sin 1 cot 2 csc 2 cos cos tan 1 sec 2 2 tan tan Verifying Trigonometric Identities To verify a trigonometric identity we must show that one side of the identity can be simplified so that it is identical to the other side or each side can be simplified independently until they are identical. Never treat an identity like an equation. We are not solving for the variable. Techniques for verifying trigonometric identities. 1) Rename using the fundamental identities. 2) Rewrite a more complicated side in terms of sines and cosines. 3) Factor. 4) Combine fractional expressions using an LCD. 5) Separate a single-term quotient into two terms. 6) Multiply the numerator and denominator on one side by a binomial factor that appears on the other side of the identity. Maeve Miranda Ryan Laurel Brent Peyton John Jessica Bianca Carson Sarah Weilun Chelsea R. Matt Katie Kevin Chelsea K. Lindsay Lindsey Rachel Jules Lisa Jenn Casey Leah Brian Hayley Kelsey Danielle Rebecca Miles Blake Eleanor Jenn Co Olivia Carola