Inverse Trig Calculator

How to Use This Calculator

1. Enter the trig value and select the inverse function (arcsin, arccos, or arctan).
2. The angle is returned in both degrees and radians.
3. Use All Quadrants to find all solutions in 0°–360°.
4. Use From Side Ratios to compute angles from triangle side lengths.

Formula

Example

Frequently Asked Questions

• What is arcsin? ▼
  arcsin(x) is the inverse sine function — it returns the angle θ such that sin(θ) = x. The principal value range is [−90°, 90°] (or [−π/2, π/2] in radians), and the domain is [−1, 1]. For example, arcsin(0.5) = 30° because sin(30°) = 0.5. arcsin(1) = 90°, arcsin(0) = 0°, arcsin(−1) = −90°. If |x| > 1, arcsin is undefined in real numbers (no real angle has a sine greater than 1). The principal range ensures each input has exactly one output.
• What is the principal value range of arccos? ▼
  arccos(x) returns angles in [0°, 180°] (or [0, π] radians). This range ensures one unique output per input (making arccos a true function). The domain is [−1, 1]. For example: arccos(1) = 0°, arccos(0) = 90°, arccos(−1) = 180°. Note that arccos and arcsin are complementary: arcsin(x) + arccos(x) = 90° = π/2 for all x in [−1, 1]. So arccos(0.5) = 60° (since arcsin(0.5) = 30° and 30 + 60 = 90).
• Why does arcsin(0.5) = 30°? ▼
  Because sin(30°) = 0.5, and arcsin is the inverse: arcsin(0.5) = 30° = π/6 radians. The arcsin function asks: "what angle has a sine of 0.5?" Only within the principal range [−90°, 90°] does 30° uniquely answer this. Note that 150° also has sin(150°) = 0.5, but 150° falls outside the principal range [−90°, 90°], so arcsin returns 30°, not 150°. To find all solutions to sin(θ) = 0.5, use: θ = 30° + 360°n or θ = 150° + 360°n.
• What is the identity arcsin(x) + arccos(x) = π/2? ▼
  For any x in [−1, 1], arcsin(x) and arccos(x) are complementary angles that always sum to π/2 radians (90°). This follows from the co-function identity: sin(θ) = cos(90° − θ). If arcsin(x) = θ, then sin(θ) = x, so cos(90°−θ) = x, meaning arccos(x) = 90° − θ. Therefore arcsin(x) + arccos(x) = θ + (90°−θ) = 90°. Example: arcsin(0.6) + arccos(0.6) ≈ 36.87° + 53.13° = 90°. ✓ This identity is useful for simplifying expressions and checking calculator results.
• What is arctan and when is it defined? ▼
  arctan(x) is the inverse tangent function — it returns the angle θ such that tan(θ) = x. Unlike arcsin and arccos, arctan is defined for all real x (the entire number line), and returns values in (−90°, 90°) (open interval, excluding the endpoints because tan is undefined there). Examples: arctan(1) = 45°, arctan(0) = 0°, arctan(−1) = −45°, arctan(√3) = 60°. As x → ∞, arctan(x) → 90°; as x → −∞, arctan(x) → −90°. arctan is used to find angles from slope ratios (opposite/adjacent) in right triangles.

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