MPT Trigonometry 5

Question 1

What is the exact value of sin(7π/6)?

Accepted Answer

-1/2

Answer

7π/6 = π + π/6 is in Q3; sin is negative, reference angle π/6 gives sin = -1/2.

Question 2

Simplify: tan²(θ) - sec²(θ).

Accepted Answer

-1

Answer

From the identity sec²(θ) = 1 + tan²(θ), it follows that tan²(θ) - sec²(θ) = -1.

Question 3

Using the Law of Sines, if A = 30°, a = 5, and B = 45°, find side b.

Accepted Answer

5√2/2

Answer

b/sin(B) = a/sin(A) → b = 5·sin(45°)/sin(30°) = 5·(√2/2)/(1/2) = 5√2.

Question 4

What is the value of sin(-π/3)?

Accepted Answer

-√3/2

Answer

Sine is an odd function, so sin(-π/3) = -sin(π/3) = -√3/2.

Question 5

Which expression equals cos²(θ) using the half-angle identity?

Accepted Answer

(1 + cos(2θ))/2

Answer

The half-angle (power-reduction) identity gives cos²(θ) = (1 + cos(2θ))/2.

(MPT) UCF Math Placement Test Practice Test