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MA 108-001 PracticeTest 3
A note about exact form or exact value: An answer in exact form is a fraction or
number written using radicals, integers, and the number π only. So, examples of exact
√
1
form numbers include 11π, √ , 13 7, and 3. Answers not in exact form include 1.25,
3π
2
1.1,
, and 1.16. If you are not sure if your answer is in exact form, you should
1.789443
check with me before turning in your exam. If you given decimal approximations when
I ask for exact values I cannot give you any points.
Problem 1 Use a sum, difference, product, or half-angle formula to find the exact value
of each expression:
(a) sin(−15◦ )
(b) cos
7π
12
(c) sin 75◦ + sin 15◦
(d) cos 22.5◦
(e) csc
7π
8
(f) sin 15◦ cos 15◦
(g) sin 75◦ cos 15◦
6
−1
(h) tan 2 sin
−
11
3
1
(i) cos2
sin−1
2
5
Problem 2
(a) Solve cos θ + sin θ = 0 for θ. Give formula(s) for the infinite solution set. State
which solutions are in the interval [0, 2π).
(b) Solve 4 sin2 (2θ) = 3 for θ. Give formula(s) for the infinite solution set. State
which solutions are in the interval [0, 2π).
1
for θ. Give formula(s) for the infinite solution set. State
2
which solutions are in the interval [0, 2π).
(c) Solve sin θ cos θ =
(d) Solve 2 sin2 θ − 3 sin θ + 1 = 0 for θ. Give formula(s) for the infinite solution set.
State which solutions are in the interval [0, 2π).
Problem 3
(a) Establish the identity sin θ tan θ + cos θ = sec θ
(b) Establish the identity
cos(α + β)
= cot β − tan α
cos α sin β