TMUA Trigonometry 5

Question 1

What is the value of cos(A - B) if sin(A) = 3/5, cos(B) = 5/13, and both A and B are acute?

Accepted Answer

56/65

Answer

cos A = 4/5, sin B = 12/13; cos(A-B) = cosAcosB + sinAsinB = (4/5)(5/13)+(3/5)(12/13) = 20/65+36/65 = 56/65.

Question 2

Which of the following is a solution to cos(2x) + cos(x) = 0 in [0, 2π]?

Accepted Answer

x = π/3

Answer

Substituting 2cos²x - 1 + cosx = 0 gives (2cosx - 1)(cosx + 1) = 0, so cosx = 1/2 → x = π/3.

Question 3

The graph of y = sin(x) is translated π/4 to the right. What is the new equation?

Accepted Answer

y = sin(x - π/4)

Answer

A rightward shift by c replaces x with x - c, giving y = sin(x - π/4).

Question 4

What is the exact value of sin(3π/4)?

Accepted Answer

√2/2

Answer

sin(3π/4) = sin(π - π/4) = sin(π/4) = √2/2.

Question 5

Which of the following identities is INCORRECT?

Accepted Answer

sin²x + cos²x = 2

Answer

The Pythagorean identity is sin²x + cos²x = 1, not 2; the other three identities are correct.

(TMUA) Test of Mathematics for University Admission Practice Test