Trigonometric Function Properties and Identities

Mathematics

This document contains a series of questions and solutions related to trigonometric functions, covering topics such as period, amplitude, simplification of expressions, solving trigonometric equations, finding domains, and evaluating exact values.

Trigonometry Algebra Functions

10 Questions Medium Ages 14+ Mar 30, 2026

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About this Study Set

This study set covers Mathematics through 10 practice questions. This document contains a series of questions and solutions related to trigonometric functions, covering topics such as period, amplitude, simplification of expressions, solving trigonometric equations, finding domains, and evaluating exact values. Every question includes the correct answer so you can learn as you go — pick any format above to get started.

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Browse all 10 questions from the Trigonometric Function Properties and Identities study set below. Each question shows the correct answer — select a study format above to practice interactively.

1 What is the period of the function f(x) = sin(4x)?

A π/2
B π
C 2π
D 4π

2 Find the amplitude of the function g(x) = 3cos(x) + 5.

3 Simplify the expression sin(θ) + cos(θ) + tan(θ) given that sin(θ) + cos(θ) = 1.

A sec(θ)
B csc(θ)
C 1
D tan(θ)

4 If sec(θ) = 2 and 270° < θ < 360°, find θ.

A 300°
B 330°
C 270°
D 360°

5 Solve for x in the interval [0, 2π]: 2sin(x) > 1.

A (π/6, 5π/6)
B [0, π/6) U (5π/6, 2π]
C (0, π/6) U (5π/6, 2π)
D [π/6, 5π/6]

6 What is the domain of the function s(x) = tan(x)?

A x ≠ nπ, n ∈ Z
B x ≠ π/2 + nπ, n ∈ Z
C x ≠ 2nπ, n ∈ Z
D x ∈ R

7 Find the exact value of sin(210°).

A -1/2
B 1/2
C -√3/2
D √3/2

8 What is the range of the function h(x) = 2sin(x) - 3?

A [-5, -1]
B [-1, 1]
C [-3, 2]
D [-2, 2]

9 Which of the following is equivalent to cos(-x)?

A cos(x)
B sin(x)
C -cos(x)
D -sin(x)

10 If cos(θ) = 1/2 and 0° < θ < 90°, what is the value of sec(θ)?

A 2
B 1/2
C √3/2
D 2/√3

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