Unit 2 Review and Quiz
A free Trigonometry lesson from the “Angles, Degrees, and Radians” unit, with a worked example and practice problems including step-by-step solutions.
This checkpoint reviews Angles, Degrees, and Radians with a mix of computation, interpretation, and transfer problems.
What you'll learn
- Convert between degrees and radians
- Find coterminal and reference angles
- Use quadrant signs to prepare for exact trig values
Worked example
Problem. Unit 2 Review and Quiz: Find the reference angle for 315 degrees.
- Locate the quadrant.
- Measure the acute angle to the x-axis.
- The reference angle is 45 degrees.
Answer: 45
Practice problems
1. Unit 2 Review and Quiz: Convert 315 degrees to radians.
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 2 Review and Quiz: Convert 315 degrees to radians.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Use 180 degrees = pi radians.
- Compute 315 * pi/180.
- The result is 7pi/4.
- Check the result by substituting or estimating: the response should match 7pi/4 and make sense in the original problem.
Answer: 7pi/4
2. Unit 2 Review and Quiz: Convert pi/3 radians to degrees.
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 2 Review and Quiz: Convert pi/3 radians to degrees.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Use pi radians = 180 degrees.
- Match the common unit-circle angle.
- Write the degree measure.
- Check the result by substituting or estimating: the response should match 60 and make sense in the original problem.
Answer: 60
3. Unit 2 Review and Quiz: Find the angle from 0 to 360 degrees coterminal with -510 degrees.
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 2 Review and Quiz: Find the angle from 0 to 360 degrees coterminal with -510 degrees.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Add or subtract full turns of 360 degrees.
- The standard coterminal angle is 210.
- The terminal side is unchanged.
- Check the result by substituting or estimating: the response should match 210 and make sense in the original problem.
Answer: 210
4. Unit 2 Review and Quiz: Find the reference angle for 315 degrees.
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 2 Review and Quiz: Find the reference angle for 315 degrees.
- Use the relevant geometric relationship first, then set up an equation from the angle measures or side relationships.
- Locate the quadrant.
- Measure the acute angle to the x-axis.
- The reference angle is 45 degrees.
- Check the result by substituting or estimating: the response should match 45 and make sense in the original problem.
Answer: 45
5. Unit 2 Review and Quiz: In Quadrant II, which basic trig function is positive?
Choices: sine · cosine · tangent · cosine and tangent
Show solution
- Checkpoint Review: First identify exactly what the question is asking: Unit 2 Review and Quiz: In Quadrant II, which basic trig function is positive?
- For function notation, treat the value inside parentheses as the input and carefully substitute it into the rule.
- Quadrant II has positive y and negative x.
- Sine follows y.
- Cosine and tangent are negative.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: sine
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