Module 3: Practice Problems
Instructions: Work each problem, then reveal the solution.
1
The point (−4, 3) is on the terminal side of θ. Find sin θ and cos θ.
Solution
r = √(16+9) = 5. sin = 3/5, cos = −4/5.
2
Evaluate sec(5π/6).
Solution
cos(5π/6) = −√3/2. sec = 1/cos = −2/√3 = −2√3/3.
3
If sin θ = −8/17 and θ in QIII, find all six trig values.
Solution
cos² = 1 − 64/289 = 225/289, cos = −15/17 (QIII). tan = 8/15. csc = −17/8, sec = −17/15, cot = 15/8.
4
Simplify: sec²θ − 1
Solution
= tan²θ (from 1 + tan² = sec²).
5
Simplify: sin(−θ)/cos(−θ)
Solution
= (−sin θ)/(cos θ) = −tan θ.
6
Evaluate cot(4π/3).
Solution
QIII, ref = π/3. cot(π/3) = 1/√3 = √3/3. Positive in QIII: √3/3.
7
Simplify: (1 + tan²θ) cos²θ
Solution
= sec²θ · cos²θ = (1/cos²θ)(cos²θ) = 1.
8
Express sin 55° as a cosine function.
Solution
sin 55° = cos 35°.
9
If tan θ > 0 and cos θ < 0, what quadrant is θ in?
Solution
QIII (tan positive, cos negative).
10
Simplify: cos(−θ) sec θ
Solution
= cos θ · (1/cos θ) = 1.