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Inverse trigonometric functions formulas
10 formulas for Inverse trigonometric functions, from the Trigonometry section of the Quantix formula library. Tap 🧮 next to a formula to solve it for any variable with step-by-step working.
| Name | Formula | Note |
|---|---|---|
| Principal ranges | sin⁻¹: [−π/2, π/2]; cos⁻¹: [0, π]; tan⁻¹: (−π/2, π/2) | |
| Complement | sin⁻¹x + cos⁻¹x = π/2 | |
| Complement | tan⁻¹x + cot⁻¹x = π/2 | |
| Complement | sec⁻¹x + cosec⁻¹x = π/2 | |
| Negative argument | sin⁻¹(−x) = −sin⁻¹x; cos⁻¹(−x) = π − cos⁻¹x | |
| Reciprocal | sin⁻¹(1/x) = cosec⁻¹x | |
| Sum of tan⁻¹ | tan⁻¹x + tan⁻¹y = tan⁻¹((x + y)/(1 − xy)), xy < 1 | |
| Difference of tan⁻¹ | tan⁻¹x − tan⁻¹y = tan⁻¹((x − y)/(1 + xy)) | |
| Double | 2tan⁻¹x = tan⁻¹(2x/(1 − x²)) = sin⁻¹(2x/(1 + x²)) | |x| < 1 |
| Double | 2sin⁻¹x = sin⁻¹(2x√(1 − x²)) |
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