Table of contents

0. Review of College Algebra(0)
1. Measuring Angles(0)
2. Trigonometric Functions on Right Triangles(0)
3. Unit Circle(0)
4. Graphing Trigonometric Functions(0)
5. Inverse Trigonometric Functions and Basic Trigonometric Equations(0)
6. Trigonometric Identities and More Equations(0)
7. Non-Right Triangles(0)
8. Vectors(0)
9. Polar Equations(0)
10. Parametric Equations(0)
11. Graphing Complex Numbers(0)

3. Unit Circle

Reference Angles

3. Unit Circle

Reference Angles - Online Tutor, Practice Problems & Exam Prep

Reference Angles Practice Problems

74 problems

1PRACTICE PROBLEM

Calculate the measurement of the reference angle for 343°.

2PRACTICE PROBLEM

Calculate the measurement of the reference angle for 11π/6.

3PRACTICE PROBLEM

Calculate the measurement of the reference angle for - 128°.

4PRACTICE PROBLEM

Calculate the measurement of the reference angle for 6.7, and express the answer in four significant figures.

5PRACTICE PROBLEM

Calculate the measurement of the reference angle for 541°.

6PRACTICE PROBLEM

Calculate the measurement of the reference angle for 8π/3.

7PRACTICE PROBLEM

Calculate the measurement of the reference angle for - 17π/6.

8PRACTICE PROBLEM

Calculate the measurement of the reference angle for - 53π/12.

9PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles, and applying the rule of signs of trigonometric functions.

cos 210°

10PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles, and applying the rule of signs of trigonometric functions.

sec 210°

11PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles, and applying the rule of signs of trigonometric functions.

sin (3π/4)

12PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles, and applying the rule of signs of trigonometric functions.

csc (4π/3)

13PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles, and applying the rule of signs of trigonometric functions.

cot (5π/3)

14PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles, and applying the rule of signs of trigonometric functions.

tan 13π/2

15PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles, and applying the rule of signs of trigonometric functions.

sin (- 210°)

16PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles.

tan (- π/6)

17PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles.

sec 855°

18PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles.

cot 10π/3

19PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles.

tan (- 8π/3)

20PRACTICE PROBLEM

Evaluate the following expression manually by using reference angles.

sin (- 35π/6)

21PRACTICE PROBLEM

Determine the exact value of the following expression without the help of the calculator. Write your answer as a single fraction.

sin (3π/2) cos (π/3) - cos (π/6) sin (3π/4)

22PRACTICE PROBLEM

Determine the exact value of the following expression without the help of the calculator. Write your answer as a single fraction.

sin (3π/4) tan (-13π/4) - cos (-7π/6)

23PRACTICE PROBLEM

Determine the exact value of (f o g) (13π/6) without the help of the calculator.

f(x) = 3x, g(x) = tan x

24PRACTICE PROBLEM

Determine the exact value of the average rate of change for the given function from x ₁ = 9π/4 to x ₂ = 5π/2 without the help of the calculator.

f(x) = cos x

25PRACTICE PROBLEM

Find the reference angle for the angle given below.

255°

26PRACTICE PROBLEM

Find the reference angle for the angle given below.

-435°

27PRACTICE PROBLEM

Find the reference angle for the angle given below.

-10π/3

28PRACTICE PROBLEM