#### Question

Find the principal value of `sin^-1(1/sqrt2)`

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#### Solution

Let `sin^-1(1/sqrt2)`

`∴ sin^-1x=(1/sqrt2)`

`∴ sin x=-sin(pi/4)`

The principal value branch of `sin^-1 x is [-pi/2,pi/2] and -pi/2<=-pi/4<=pi/2`

Hence, the required principal value of x is `-pi/4`

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#### Reference Material

Solution for question: Find the principal value of sin-1(1/sqrt2) concept: Basic Concepts of Trigonometric Functions. For the courses HSC Science (Electronics), HSC Science (Computer Science), HSC Science (General) , HSC Arts