Tag
trigonometry
- 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 Evaluate Trig Functions Without a CalculatorUse the unit circle, reference angles, identities, and Taylor series to find exact or accurate trigonometric values without a calculator.
- How to Calculate Compound Angles in TrigonometryUse compound-angle identities to find sine, cosine, or tangent of sums and differences, with sign rules and a worked exact-value example.
- How to Calculate Sine and Cosine Without a CalculatorLearn exact values for common angles and approximate other sine, cosine, and tangent values by reducing the angle and using Taylor series by hand.
- How to Calculate Sine by Hand Without a CalculatorCalculate sine by hand using exact values for common angles or a Taylor series for any angle, with angle reduction, a worked example, and an error bound.
- How to Compute the Sine of Huge NumbersFor huge angles, compute sine by reducing the input modulo 2π. Learn why ordinary floating-point remainder can fail and when to use high precision.
- 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.
- When Should Your Calculator Be in Radian or Degree Mode?Use degree mode for angles marked ° and radian mode for angles in radians, such as π/6. Convert mismatched inputs; inverse-trig answers use the selected mode.
- How to Write a Trigonometric Expression in Sine and CosineReplace tangent, cotangent, secant, and cosecant with sine-and-cosine quotients, then simplify; the exact expression is needed for a unique answer.