Study Guide – Double angles and Sum and Difference Identities – sections 7.1 and 7.2
NAME______________________________
Simplify the given expressions. Give exact answers! – only fractions, no decimals!
1.) sin (x + 60) + sin (x – 60)
1.) ___________________________
2.) cos (30 + y) - cos (30 – y)
2.) ___________________________
3 and 4.) If sin C = 5/13 and sin D = 1/2 and 0 < C < π/2 < D < π, find:
3.) sin (C - D)
3.) ___________________________
4.) cos (C + D)
4.) ___________________________
5.) Prove (in at least two steps) that the given equation is an identity:
6.) Simplify
sin (π – x) = sin x
sin( x + 30) + sin( x − 30)
cos(30 + x) + cos(30 − x)
6.) __________________________
7.) Simplify
tan 8 x − tan 2 x
1 + tan 8 x tan 2 x
7.) __________________________
8.) If cos x = 3/5 and cos y = √2/2 and 0 < y < x < π/2 find tan (x - y)
8.) __________________________
9.) Simplify: cos 3y cos y + sin 3y sin y
9.) _________________________
10.) Simplify: sin 36θ cos 8θ + cos 36θ sin 8θ
10.) ________________________
11.) Simplify:
tan x + tan 6 x
1 − tan x tan 6 x
11.) ________________________
Using the values from common trig angles like 30º, 45º, 60º, 90º, 120º, etc., determine the EXACT (fractional)
values for:
12.) sin 75º
12.) ________________________
13.) cos 15º
13.) _______________________
14.) tan 225º
14.) ________________________
Simplify.
15.) 3 - 6 sin2 14º =
15.)
16.)
− 8 tan 32°
=
1 − tan 2 32°
16.)
17.) 4 cos 17º sin 17º =
17.)
18.)
− 4 sin 2 77° + 4 cos 2 77°
=
8
18.)
19.) If tan B = 5/12 , find the EXACT value of sin 2B and cos 2B.
19a.) sin 2B =
19b.) cos 2B =
20.) If sin A = 2/3 , find the EXACT value of cos 2A and cos 4A
20a.) cos 2A =
20b.) cos 4A =
Find the EXACT value for 7 and 8.
4 tan
21.)
1 − tan
π
12
2
π
=
12
21.)
22.) 8 sin 135º cos 135º =
22.)
Prove that the left hand side equals the right hand side for 9 and 10.
23.)
sin 2 A
= 2 cot A
sin 2 A