TMUA Trigonometry 2

Question 1

Which of the following is equal to sin(π - x)?

Accepted Answer

sin(x)

Answer

By the identity sin(π - x) = sin(x), the answer is sin(x).

Question 2

If cos(θ) = 3/5 and θ is in the fourth quadrant, what is sin(θ)?

Accepted Answer

-4/5

Answer

Using sin²θ + cos²θ = 1 gives |sin θ| = 4/5, and since θ is in Q4, sin θ = -4/5.

Question 3

What is the period of the function f(x) = tan(3x)?

Accepted Answer

π/3

Answer

The period of tan(kx) is π/k, so for k = 3 the period is π/3.

Question 4

Simplify: (1 - cos²x) / sin(x), for sin(x) ≠ 0.

Accepted Answer

sin(x)

Answer

Since 1 - cos²x = sin²x, dividing by sin(x) gives sin(x).

Question 5

What is the exact value of cos(150°)?

Accepted Answer

-√3/2

Answer

cos(150°) = cos(180° - 30°) = -cos(30°) = -√3/2.

(TMUA) Test of Mathematics for University Admission Practice Test