Trigonometry Flashcards

What is the exact value of sin(7π/6)?

Answer: -1/2

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

Simplify: tan²(θ) - sec²(θ).

Answer: -1

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

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

Answer: 5√2/2

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

What is the value of sin(-π/3)?

Answer: -√3/2

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

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

Answer: (1 + cos(2θ))/2

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

The graph of y = cos(x) is shifted left by π/2. What is the resulting function?

Answer: Both A and C

cos(x + π/2) = -sin(x), but the shifted graph equals sin(x) only after sign check; both A and C are equivalent and correct.

Solve for θ in [0, 2π): 2cos(θ) - 1 = 0.

Answer: θ = π/3, 5π/3

cos(θ) = 1/2 gives θ = π/3 in Q1 and θ = 5π/3 in Q4.