Question

sin^-1 ( sin3pi÷4).find the value​

Answer 1

Question:-

Question:-

$\to \: \bf \: \sin {}^{ - 1} ( \sin\frac{3\pi}{4} )$

Solution:-

$\to \: \bf \: \sin {}^{ - 1} ( \sin\frac{3\pi}{4} )$

Write the sin in the from of (2n + 1 )π - Θ, we get

$\to \: \bf \: \sin {}^{ - 1} ( \sin\pi - \frac{\pi}{4} )$

Its lies on second quadrant:- In second quadrant sinΘ will be +ve

$\to \: \bf \: \sin {}^{ - 1} ( \sin \frac{\pi}{4} )$

Now using Inverse trigonometry property

$\to \bf \: \sin {}^{ - 1} ( \sin \: x ) = x$

By using this property we get

$\to \: \bf \: \sin {}^{ - 1} ( \sin \frac{\pi}{4} ) = \frac{\pi}{4}$

Answer :- 45⁰ or π/4