Inverse Trigonometric Functions — Formula Sheet

sin⁻¹x + cos⁻¹x = π/2

tan⁻¹x + cot⁻¹x = π/2

sec⁻¹x + cosec⁻¹x = π/2

sin⁻¹(−x) = −sin⁻¹x

cos⁻¹(−x) = π − cos⁻¹x

tan⁻¹x + tan⁻¹y = tan⁻¹((x + y)/(1 − xy)), if xy < 1

sin⁻¹x + sin⁻¹y = sin⁻¹(x√(1−y²) + y√(1−x²)), if x² + y² ≤ 1

cos⁻¹x + cos⁻¹y = cos⁻¹(xy − √(1−x²)√(1−y²))

The graph of y = sin⁻¹(x) is increasing and lies between −π/2 and π/2.

y = cos⁻¹(x) decreases from π to 0 as x goes from −1 to 1.

sin⁻¹(x) + cos⁻¹(x) = π/2 for all x ∈ [−1, 1].

tan⁻¹(x) + cot⁻¹(x) = π/2.

Important identities include sin⁻¹x + cos⁻¹x = π/2, tan⁻¹x + cot⁻¹x = π/2, and tan⁻¹x + tan⁻¹y = tan⁻¹[(x+y)/(1−xy)] for xy < 1.