Enrich · Mathematics Extension 1 11–12 – Year 12 · Inverse trigonometric functions

Enrich Examine the graphs of the composite functions y = sin⁡(sin^(- 1)⁡x), y = cos⁡(cos^(- 1)⁡x) and y = tan⁡(tan^(- 1)⁡x), establish the values of x for which the formulas sin⁡(sin^(- 1)⁡x) = x, cos⁡(cos^(- 1)⁡x) = x and tan⁡(tan^(- 1)⁡x) = x are true, and apply the formulas to solve problems, simplify expressions and prove results

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