Tag
Inverse trigonometric functions
- Expressions for sin(arctan x) and cos(arctan x) Without Trig FunctionsUsing the principal range of arctan, sin(arctan x) = x/√(1+x²) and cos(arctan x) = 1/√(1+x²) for every real x.
- How to Calculate Inverse Trig Functions Without a CalculatorUse principal ranges, exact unit-circle values, identities, and power series to evaluate inverse sine, cosine, and tangent by hand.
- How to Calculate Arcsine Without a CalculatorFind exact inverse-sine values from special angles, or approximate arcsin(x) by a convergent power series with a practical error bound.
- How to Find the Inverse Cosine Without a CalculatorFind an inverse cosine by recognizing unit-circle values, using symmetry, or converting arccos to an arctangent and evaluating its series by hand.