1 Answer

Nanthakumar J J · Answer 1 · 2022-07-31T08:40:06+0000

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
or
.

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