S3H Unit 6C – Double Angle Identities Notes
(Worksheet 6C-3)
There are several multiple-Angle formulas in Trig. The most commonly used multiple-angle formulas are the
double angle formulas.
These are listed as #6 on your blue memorization sheet. Rewrite them here:
sin 2u =
cos 2u =
Using the Pythagorean identities you can get 2 more ways to write the cos 2u identity:
cos 2u =
cos 2u =
There are also 2 formulas for tan 2u, although these are not used as much
tan2u =
tan 2u =
Use these formulas to obtain other multiple angle formulas:
1. sin 4u =
2. cos 6u =
Rewrite the following using double angle formulas:
3. 6𝑐𝑐𝑐𝑐𝑐𝑐 2 𝑥𝑥 − 3
4. 8 sin 𝑥𝑥 cos 𝑥𝑥
5. Use this triangle to find the following:
sin u =
sin 2u =
csc 2u =
cos u =
cos 2u =
sec 2u =
tan u =
tan 2u =
cot 2u =
2
6. Find the exact values of sin 2u, cos 2u and tan2u if sin u = 3,
7. Verify the identity:
1 − 𝑡𝑡𝑡𝑡𝑡𝑡2 𝑥𝑥
= cos 2𝑥𝑥
1 + 𝑡𝑡𝑡𝑡𝑡𝑡2 𝑥𝑥
𝜋𝜋
2
< 𝑢𝑢 < 𝜋𝜋