Trigonometry Calculator
Inverse trigonometric functions (arcsin, arccos, arctan) find the angle given a ratio. arcsin(x) asks "what angle has sine = x?" They are essential for solving triangles when side lengths are known but angles are not.
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Tip: Use atan2(y, x) in programming instead of atan(y/x) — it correctly handles all quadrants and avoids division by zero when x=0. Most programming languages provide atan2 as a built-in function.
- 1arcsin(x): returns angle whose sine is x, range [−90°, 90°]
- 2arccos(x): returns angle whose cosine is x, range [0°, 180°]
- 3arctan(x): returns angle whose tangent is x, range (−90°, 90°)
- 4arctan2(y,x): full-circle angle from coordinates (−180° to 180°)
arcsin(0.5)=30°sin(30°) = 0.5
arctan(1)=45°tan(45°) = 1
arccos(0)=90°cos(90°) = 0
| Function | Domain (input) | Range (output angle) |
|---|---|---|
| arcsin(x) | [−1, 1] | [−90°, 90°] |
| arccos(x) | [−1, 1] | [0°, 180°] |
| arctan(x) | (−∞, ∞) | (−90°, 90°) |
| arccsc(x) | |x| ≥ 1 | [−90°, 90°], x≠0 |
| arcsec(x) | |x| ≥ 1 | [0°, 180°], x≠90° |
| arccot(x) | (−∞, ∞) | (0°, 180°) |
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Fun Fact
The arctan function appears in many probability distributions — the Cauchy distribution uses arctan in its CDF. It also appears in physics for calculating angles in projectile motion, optics (Brewster's angle), and electrical engineering (phase angles).
References
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