PRE CALCULUS Trigonometry 4

Question 1

What is the exact value of cos(7π/4)?

Accepted Answer

√2/2

Answer

7π/4 is in the fourth quadrant with reference angle π/4, and cosine is positive in Q4, so cos(7π/4) = √2/2.

Question 2

Which of the following is an odd function?

Accepted Answer

f(x) = sin(x)

Answer

sin(-x) = -sin(x) satisfies the definition of an odd function, f(-x) = -f(x).

Question 3

For the equation 2sin(x) - 1 = 0 on [0, 2π), the solutions are:

Accepted Answer

π/6 and 5π/6

Answer

2sin(x) = 1 gives sin(x) = 1/2, which is true at x = π/6 and x = π - π/6 = 5π/6 in [0, 2π).

Question 4

The product-to-sum formula converts sin(A)cos(B) into:

Accepted Answer

[sin(A+B) + sin(A-B)]/2

Answer

The product-to-sum identity gives sin(A)cos(B) = [sin(A+B) + sin(A-B)]/2.

Question 5

A point on the unit circle at angle θ has coordinates (cos θ, sin θ). At θ = 2π/3, the coordinates are:

Accepted Answer

(-1/2, √3/2)

Answer

2π/3 = 180° - 60°; in Q2, cosine is negative and sine is positive, giving (-1/2, √3/2).

PRE CALCULUS Practice Test