Trigonometry Core Concepts 3

Question 1

What does the Pythagorean identity state?

Accepted Answer

sin²θ + cos²θ = 1

Answer

The fundamental Pythagorean identity sin²θ + cos²θ = 1 follows directly from the unit circle definition.

Question 2

What is the range of the sine function?

Accepted Answer

[-1, 1]

Answer

The sine function oscillates between -1 and 1 inclusive for all real inputs.

Question 3

If cos(θ) = 3/5, what is sin(θ) for θ in Quadrant I?

Accepted Answer

4/5

Answer

Using sin²θ + cos²θ = 1: sin²θ = 1 - 9/25 = 16/25, so sin(θ) = 4/5 in Q I.

Question 4

What is the amplitude of y = 3sin(x)?

Accepted Answer

3

Answer

The amplitude is the absolute value of the coefficient in front of the trig function, which is 3.

Question 5

Which angle has a tangent value that is undefined?

Accepted Answer

90°

Answer

At 90°, cos(90°) = 0, making tan(90°) = sin/cos = 1/0, which is undefined.

Trigonometry Practice Test