TMUA Trigonometry 4

Question 1

In a triangle with sides a = 5, b = 7, and included angle C = 60°, what is side c?

Accepted Answer

√39

Answer

By the cosine rule: c² = 25 + 49 - 2(5)(7)cos60° = 74 - 35 = 39, so c = √39.

Question 2

Which of the following is the correct expression for the area of a triangle with sides a, b and included angle C?

Accepted Answer

(1/2)ab·sin(C)

Answer

The area formula using two sides and the included angle is Area = (1/2)ab·sin(C).

Question 3

What is the value of arcsin(sin(5π/6))?

Accepted Answer

π/6

Answer

sin(5π/6) = 1/2, and arcsin returns values in [-π/2, π/2], so arcsin(1/2) = π/6.

Question 4

If tan(x) = -√3 and x ∈ [π/2, π], what is x?

Accepted Answer

2π/3

Answer

tan(x) = -√3 and x is in Q2, so x = π - π/3 = 2π/3.

Question 5

Which identity correctly represents cos²(x) in terms of cos(2x)?

Accepted Answer

(1 + cos(2x))/2

Answer

From cos(2x) = 2cos²x - 1, rearranging gives cos²x = (1 + cos2x)/2.

(TMUA) Test of Mathematics for University Admission Practice Test