EasyMathematicsHigh School (11–12)Trigonometry › Inverse Trigonometric FunctionsNumericalBoard Exam

Find sin(cos⁻¹8/17), tan(sin⁻¹5/13) and cos(tan⁻¹3/4). Give each to four decimal places.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Find $\sin\left(\cos^{-1}\dfrac{8}{17}\right)$ , $\tan\left(\sin^{-1}\dfrac{5}{13}\right)$ and $\cos\left(\tan^{-1}\dfrac{3}{4}\right)$ . Give each to four decimal places.

Need a reminder? The key ideaShow

Draw a right triangle for the inverse function. Then $\sin(\cos^{-1}x) = \sqrt{1 - x^2}$ , $\sin(\tan^{-1}x) = \dfrac{x}{\sqrt{1 + x^2}}$ and $\cos(\tan^{-1}x) = \dfrac{1}{\sqrt{1 + x^2}}$ . For a sum of two angles use the addition formula.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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Find sin(cos⁻¹8/17), tan(sin⁻¹5/13) and cos(tan⁻¹3/4). Give each to four decimal places.

The worked solution

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