Question

An angle θ on the unit circle has a sine of 14. What is the value of cosθ?

Answer 1

Given:

An angle θ on the unit circle has a sine of
`(1)/(4)`.

To find:

The value of cosθ.

Solution:

We have,

`\sin \theta=(1)/(4)`

Since sinθ is positive, therefore, θ lies in first or second quadrant.

We know that,

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

`((1)/(4))^2+\cos^2 \theta =1`

`(1)/(16)+\cos^2 \theta =1`

`\cos^2 \theta =1-(1)/(16)`

Taking square root on both sides.

`\cos \theta =\pm \sqrt{(16-1)/(16)}`

`\cos \theta =\pm (√(15))/(4)`

Therefore, the value of cosθ is either
`(√(15))/(4)` or
`-(√(15))/(4)`.