5.2(c) Notes: A Bit of Calculus in Verifying Trig Identities Date: 5.2(c) Notes: A Bit of Calculus in Verifying Trig Identities   Lesson Objective: Verify trig identities. CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle. You will need: your trig identities cheat sheet

Lesson 1: Changing to Sines and Cosines Verify the identity:   Verify the identity: sec x + csc(-x) = sin x – cos x sec x csc x

Lesson 2: Working with Both Sides Separately Verify the identity:   Verify the identity: 1 + 1 = 2 + 2 tan2 θ 1 + sin θ 1 – sin θ

Lesson 3: Two Examples from Calculus   (a) Use a graphing utility to graph each side of the equation to determine whether the equation is an identity, (b) use the table feature of a graphing utility to determine whether the equation is an identity, and (c) confirm parts (a) and (b) algebraically. tan4 x = tan² x sec² x – tan² x

Lesson 3: Two Examples from Calculus   (a) Use a graphing utility to graph each side of the equation to determine whether the equation is an identity, (b) use the table feature of a graphing utility to determine whether the equation is an identity, and (c) confirm parts (a) and (b) algebraically. csc4 x cot x = csc² x(cot x + cot3 x)

Lesson 4: Use Cofunction to Evaluate   Use the cofunction identities to evaluate the expression without the aid of a calculator. cos² 55° + cos² 35°

5.2(c): Do I Get It? Yes or No Verify the identity. tan x + cot x = sec x csc x cot² θ + 1 – sin θ 1 + csc θ sin θ sin3 x cos4 x = (cos4 x – cos6 x) sin x sin² 12° + sin² 40° + sin² 50° + sin² 78°