Unit circle definitions; Pythagorean identity; ambiguous case practice questions.

State the exact value of cos(120°).

• −1/2
• 1/2
• −√3/2
• √3/2

Answer: −1/2

120° lies in the second quadrant where cosine is negative; the reference angle is 60°, so cos(120°) = −cos(60°) = −1/2.

Given that sin θ = 3/5 and θ is obtuse, determine cos θ.

• −4/5
• 4/5
• −3/4
• 3/4

Answer: −4/5

By the Pythagorean identity cos²θ = 1 − 9/25 = 16/25, so cos θ = ±4/5; an obtuse angle is in the second quadrant where cosine is negative, giving −4/5.

In triangle ABC, angle A = 35°, side a = 6 cm and side b = 9 cm. Using the sine rule, this ambiguous case gives how many possible triangles?

• 2
• 0
• 1
• 3

Answer: 2

sin B = b·sin A / a = 9·sin35°/6 ≈ 0.860, so B ≈ 59.4° or 120.6°; since a < b and both values keep A + B < 180°, two triangles are possible.

Determine the exact value of tan(135°).

• −1
• 1
• −√3
• −1/√3

Answer: −1

135° is in the second quadrant where tangent is negative; the reference angle is 45°, so tan(135°) = −tan(45°) = −1.

The point where the terminal side of angle θ meets the unit circle has coordinates (−0.6, 0.8). State sin θ.

• 0.8
• −0.6
• −0.8
• 0.6

Answer: 0.8

On the unit circle the point is (cos θ, sin θ), so the y-coordinate 0.8 is sin θ.

Given cos θ = −0.28, calculate sin²θ.

• 0.9216
• 0.0784
• 0.72
• 1.0784

Answer: 0.9216

By the Pythagorean identity sin²θ = 1 − cos²θ = 1 − 0.0784 = 0.9216.