Differentiation of inverse trigonometric functions (HSC SSCE Mathematics Extension 1): Flashcards

Functions that reverse trigonometric ratios to find angles.

The domain of arcsin is [-1, 1].

The range of arccos is [0, π].

The range of arctan is [-π/2, π/2].

d/dx[arcsin(x)] = 1/√(1-x²).

d/dx[arccos(x)] = -1/√(1-x²).

d/dx[arctan(x)] = 1/(1+x²).

dy/dx = 2/√(1-4x²).

They help solve integrals and differential equations.

∫1/(1+x²) dx = arctan(x) + C.