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.

← All Problems

← Show that tan⁻¹1/3 + tan⁻¹1/5 + tan⁻¹1/7 + tan⁻¹1/8 is a simple angle…Let α = tan⁻¹3/4 and β = sin⁻¹5/13. Find sin(α + β), cos(α + β) and tan(α + β)… →

More onTrigonometry › Inverse Trigonometric Functions

Discussion (0)

Loading…

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

The worked solution

Discussion (0)

Want to go further in Trigonometry › Inverse Trigonometric Functions?