Name: Multiple Angle Formula for Sine Inverse Function
Uploaded: 2019-07-19
Duration: 6 min 56 s
Description: What is twice of sine inverse function? Can we develop a formula for it? How to solve the problem using this function? Check out this video to know more.

Question

Evaluate the following inverse trigonometric expressions.

(i) $\sin^{- 1} (\sin \frac{7 π}{6})$

(ii) $\tan^{- 1} (\tan \frac{2 π}{3})$

(iii) $\cos^{- 1} (\cos \frac{5 π}{4})$

(iv) $\sec^{- 1} (\sec \frac{7 π}{4})$

Accepted Answer

(i) $\sin^{- 1} (\sin \frac{7 π}{6})$

Let $y = \sin^{- 1} (\sin \frac{7 π}{6})$

$\cos^{- 1} (\cos \frac{5 π}{4})$

$\sin y = \sin (π + \frac{π}{6})$ $[∵ \frac{7 π}{6} \notin [- \frac{π}{2}, \frac{π}{2}]]$

$\sin y = - \sin \frac{π}{6}$

$\sin y = \sin (- \frac{π}{6})$

$\Rightarrow y = - \frac{π}{6}$

(ii) $\tan^{- 1} (\tan \frac{2 π}{3})$

Let $y = \tan^{- 1} (\tan \frac{2 π}{3})$

$\Rightarrow \tan y = \tan (\frac{2 π}{3})$

$\tan y = \tan (π - \frac{π}{3})$ $[∵ \frac{2 π}{3} \notin (- \frac{π}{2}, \frac{π}{2})]$

$\tan y = - \tan \frac{π}{3}$

$\tan y = \tan (- \frac{π}{3})$

$\Rightarrow y = - \frac{π}{3}$

(iii) $\cos^{- 1} (\cos \frac{5 π}{4})$

Let $y = \cos^{- 1} (\cos \frac{5 π}{4})$

$\cos y = \cos \frac{5 π}{4} [∵ \frac{5 π}{4} \notin [0, π]]$

$\cos y = \cos (2 π - \frac{3 π}{4})$

$\cos y = \cos \frac{3 π}{4}$

$\Rightarrow y = \frac{3 π}{4}$

(iv) $y = \sec^{- 1} (\sec \frac{7 π}{4})$

$\sec y = \sec (\frac{7 π}{4})$ $[∵ \frac{7 π}{4} \notin [0, π]]$

$= \sec (2 π - \frac{π}{4})$

$\sec y = \sec \frac{π}{4}$

$\Rightarrow y = \frac{π}{4}$ .

Evaluate the following inverse trigonometric expressions.

(i) $\sin^{- 1} (\sin \frac{7 π}{6})$

(ii) $\tan^{- 1} (\tan \frac{2 π}{3})$

(iii) $\cos^{- 1} (\cos \frac{5 π}{4})$

(iv) $\sec^{- 1} (\sec \frac{7 π}{4})$

Important Questions on Inverse Trigonometric Functions

Learn and Prepare for any exam you want !

Evaluate the following inverse trigonometric expressions. (i) sin-1sin7π6 (ii) tan-1tan2π3 (iii) cos-1cos5π4 (iv) sec-1sec7π4

Important Questions on Inverse Trigonometric Functions

Learn and Prepare for any exam you want !

Evaluate the following inverse trigonometric expressions.

(i) $\sin^{- 1} (\sin \frac{7 π}{6})$

(ii) $\tan^{- 1} (\tan \frac{2 π}{3})$

(iii) $\cos^{- 1} (\cos \frac{5 π}{4})$

(iv) $\sec^{- 1} (\sec \frac{7 π}{4})$