Inverse Trigonometric Functions
A free Algebra II lesson from the “Trigonometry and Modeling” unit, with a worked example and practice problems including step-by-step solutions.
Inverse trig functions answer 'which angle has this trig value?' arcsin (also written sin^-1) undoes sin; arccos undoes cos; arctan undoes tan. To make the inverse a function, each one returns only the PRINCIPAL value: arcsin in [-90, 90], arccos in [0, 180], arctan in (-90, 90) (degrees).
What you'll learn
- Evaluate arcsin, arccos, and arctan for common input values
- Know the principal-value ranges: arcsin in [-90, 90], arccos in [0, 180], arctan in (-90, 90) degrees
- Use inverse trig to solve simple right-triangle problems
Worked example
Problem. Evaluate arcsin(1/2) in degrees.
- Ask: sin of what angle equals 1/2?
- sin(30 degrees) = 1/2 -> arcsin(1/2) = 30 degrees.
Answer: 30
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. arcsin(0) in degrees.
Show solution
- sin(0) = 0.
Answer: 0
2. arcsin(1) in degrees.
Show solution
- sin(90) = 1.
Answer: 90
3. arcsin(1/2) in degrees.
Show solution
- sin(30) = 1/2.
Answer: 30
4. arccos(1) in degrees.
Show solution
- cos(0) = 1.
Answer: 0
5. arccos(0) in degrees.
Show solution
- cos(90) = 0.
Answer: 90
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