1. 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

2. 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

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

4. 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

5. 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)

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

7. 5.2(c): Do I Get It? Yes or No
Verify the identity.
tan x + cot x = sec x csc x
cot² θ – 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°