Question

If sin square theta = 0.75, then cos =

Answer 1

`\cos\theta=\pm0.5`

Explanation:

Given:

`\sin^2\theta=0.75`

To find
`\cos\theta`

Using trigonometric relations for sums and differences of squares of the ratios.

We know:

`\sin^2\theta+\cos^2\theta =1`

Plugging in
`\sin^2\theta=0.75` in the above relation.

`0.75+\cos^2\theta =1`

Subtracting both sides by 0.75.

`0.75+\cos^2\theta-0.75 =1-0.75`

`\cos^2\theta =0.25`

Taking square root both sides.

`√(\cos^2\theta) =√(0.25)`

∴
`\cos\theta=\pm0.5` (Answer)