COMPASS College Algebra and Trigonometry 3

Question 1

What is the Pythagorean identity in trigonometry?

Accepted Answer

sin²θ + cos²θ = 1

Answer

The fundamental Pythagorean identity is sin²θ + cos²θ = 1, derived from the unit circle.

Question 2

Find the zeros of f(x) = x³ − x

Accepted Answer

x = 0, 1, −1

Answer

Factor: x(x² − 1) = x(x − 1)(x + 1) = 0, giving x = 0, 1, −1.

Question 3

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

Accepted Answer

4

Answer

The amplitude of y = A sin(x) is |A|, which equals 4.

Question 4

Solve: 2^(x+1) = 16

Accepted Answer

3

Answer

16 = 2⁴, so 2^(x+1) = 2⁴ means x + 1 = 4, giving x = 3.

Question 5

Which transformation shifts y = f(x) up by 3 units?

Accepted Answer

y = f(x) + 3

Answer

Adding a constant outside the function shifts the graph vertically upward.

COMPASS Practice Test