Trigonometry Advanced Trigonometric Concepts 3

Question 1

Simplify: (1 - cos²θ) / sinθ

Accepted Answer

sinθ

Answer

1 - cos²θ = sin²θ by the Pythagorean identity, so sin²θ / sinθ = sinθ.

Question 2

What is the phase shift of y = cos(2x + π/3)?

Accepted Answer

-π/6

Answer

Phase shift = -C/B = -(π/3)/2 = -π/6, shifting the graph left by π/6.

Question 3

Using the law of cosines, if a = 5, b = 7, and C = 60°, what is c²?

Accepted Answer

39

Answer

c² = a² + b² - 2ab cosC = 25 + 49 - 2(5)(7)(0.5) = 74 - 35 = 39.

Question 4

Which of the following is the correct half-angle formula for sin(θ/2)?

Accepted Answer

±√((1 - cosθ)/2)

Answer

The half-angle formula for sine is sin(θ/2) = ±√((1 - cosθ)/2).

Question 5

What is the value of cos⁻¹(cos(5π/4))?

Accepted Answer

3π/4

Answer

cos(5π/4) = -√2/2, and arccos(-√2/2) = 3π/4 since arccos outputs values in [0, π].

Trigonometry Practice Test