Inverse trigonometric functions calculator
Find the angle whose sine, cosine or tangent is a given value.
Enter your values and press Calculate. Your inputs stay in the address, so you can switch language or share the link.
Formula
θ = sin⁻¹(x) or cos⁻¹(x) or tan⁻¹(x)
How it works
sin⁻¹ and cos⁻¹ only accept values from −1 to 1, since sine and cosine never go outside that range; tan⁻¹ accepts any value.
Worked example
The same calculation with the default values:
- Function sin⁻¹ (arcsine)
- Value 0.5
- θ = asin(0.5) = 0.523599 rad
- θ = 0.523599 × 180 ÷ π = 30°
Result: Angle (radians): 0.52359878 rad · Angle (degrees): 30 °
Each inverse trig function returns only one angle (the principal value) even though infinitely many angles share the same sine, cosine, or tangent - sin⁻¹ and cos⁻¹ are restricted to the range that makes them single-valued, which may not be the specific angle a real geometry problem needs.
Common mistakes
- Entering a value outside [-1, 1] for sin⁻¹ or cos⁻¹ - sine and cosine never exceed this range, so no real angle exists for an input outside it.
- Forgetting that the result may need adjusting by adding or subtracting from 180° (or π) to get the actual angle needed in a specific triangle or context - the principal value isn't automatically the "right" quadrant for every problem.
- Confusing degrees and radians in the output - this calculator's unit must match what the rest of the problem is using, or every downstream calculation will be off by a factor of roughly 57.3.
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