PRE CALCULUS Pre-Calculus Trigonometry 2

Question 1

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

Accepted Answer

2π/3

Answer

The period of sin(bx) is 2π/b, so for b=3 the period is 2π/3.

Question 2

Which identity correctly expresses cos(2θ) in terms of sin(θ) only?

Accepted Answer

1 − 2sin²θ

Answer

Using cos(2θ) = cos²θ − sin²θ and cos²θ = 1 − sin²θ gives 1 − 2sin²θ.

Question 3

What is the amplitude of y = −4cos(x)?

Accepted Answer

4

Answer

Amplitude is the absolute value of the leading coefficient, so |−4| = 4.

Question 4

In which quadrant is the angle 210° located, and what is the sign of its tangent?

Accepted Answer

Quadrant III, positive

Answer

210° is in Quadrant III where both sine and cosine are negative, making tangent positive.

Question 5

What is the exact value of csc(π/6)?

Accepted Answer

2

Answer

csc(π/6) = 1/sin(π/6) = 1/(1/2) = 2.

PRE CALCULUS Practice Test