Question

If sin x=-√2/2 and cos x=√2/2 the measure of angle x is

Answer 1

Explanation:

We have,

`\sin x=-(\sqrt2)/(2)\ ......(i)`

`\cos x=(\sqrt 2)/(2)\ ......(ii)`

Applying
`\sin^(-1)` on both sides of equation (i) we get :

`\sin^(-1) \sin x=\sin^(-1)(-(\sqrt2)/(2))`

We know that,
`\sin^(-1) \sin x=x`

So,

`x=\sin^(-1)(-(\sqrt2)/(2))`

Also,
`\sin(-45)=(-\sqrt2)/(2)`

So,

`x=-45^(\circ)`

Similarly,

Applying
`\cos^(-1)` on both sides of equation (ii) we get :

`\cos^(-1) \cos x=\cos^(-1)((\sqrt2)/(2))`

We know that,
`\cos^(-1) \cos x=x`

The cosine function is positive in the first and fourth quadrant.

So,

`x=45^(\circ)`