1. Ch 5.2

2. Check your hw with your groups! I will walk around and answer questions. If you are all done, start the Warm Up Ch 5.2 on a blank piece of lined paper
Match the trigonometric expression with one of the following
csc(x) b) tan(x) c) sin²(x) d) sin(x)tan(x) e) sec²(x) f) sec²(x) +tan²(x)
sin(x)sec(x) = 4) cot(x)sec(x)
2) cos²(x)[sec²(x)-1] 5) sec²(x)−1 sin²(x)
3) 𝑠𝑒𝑐 4 (x) - 𝑡𝑎𝑛 4 (x) 6) cos²[ π 2 −𝑥] cos(x)
Check your answers with your partner!

3. Guidelines for Verifying Trig Identities
Ch 5.2 Notes
Guidelines for Verifying Trig Identities
1) Work with one side of the equation at a time Use the more complicated side first 2) Look for opportunities to factor the expression, add fractions, square a binomial, or create a monomial denominator 3) Look for opportunities to use the fundamental identities 4) If nothing is working, try converting all terms to sines and cosines 5) ALWAYS try SOMETHING

4. Why is verifying trig identities useful?
It is a useful process for converting a trigonometric expression into a form that is more useful algebraically.

5. EX 1: Verify the identity 𝑠𝑒𝑐 2 𝑥 −1 𝑠𝑒𝑐 2 𝑥 = 𝑠𝑖𝑛 2 𝑥
Because the left side is more complicated, start with it.
𝑠𝑒𝑐 2 𝑥 −1 𝑠𝑒𝑐 2 𝑥 = [𝑡𝑎𝑛 2 𝑥 +1]−1 𝑠𝑒𝑐 2 𝑥 Use the Pythagorean Identity
= 𝑡𝑎𝑛 2 𝑥 𝑠𝑒𝑐 2 𝑥 Simplify
= 𝑡𝑎𝑛 2 𝑥 𝑐𝑜𝑠 2 (x) use the Reciprocal identity
= 𝑠𝑖𝑛 2 𝑥 𝑐𝑜𝑠 2 𝑥 𝑐𝑜𝑠 2 (x) use quotient identity
= 𝑠𝑖𝑛 2 (x) simplify

6. EX 2: Hint: add fractions
Hint: Apply Pythagorean
Identities first before multiplying
Verify
( 𝑡𝑎𝑛 2 𝑥 +1)( 𝑐𝑜𝑠 2 𝑥 -1) = - 𝑡𝑎𝑛 2 𝑥
Verify 1 (1− sin 𝑥 ) (1+ sin 𝑥 ) = 2 𝑠𝑒𝑐 2 (x)

7. You Try! Verify each identity
1) Sin(x) csc(x) = ) [1 + sin(x)] [1 – sin(x)] = cos²(x)
2) 𝑠𝑖𝑛²(𝑥) tan²(𝑥) =𝑐𝑜𝑠²(𝑥) ) 𝑡𝑎 𝑛 2 𝑥 [ 𝑐𝑠 𝑐 2 𝑥 −1 ] = 1

8. Describe each error (textbook pg 365)
19) Cot(-x) = -cot(x)
20) sec(-x) = sec(x) and sin(-x) = sin(x)

9. Setting up the table of contents…