Given:
An angle θ on the unit circle has a sine of [tex]\dfrac{1}{4}[/tex].
To find:
The value of cosθ.
Solution:
We have,
[tex]\sin \theta=\dfrac{1}{4}[/tex]
Since sinθ is positive, therefore, θ lies in first or second quadrant.
We know that,
[tex]\sin^2 \theta +\cos^2 \theta =1[/tex]
[tex](\dfrac{1}{4})^2+\cos^2 \theta =1[/tex]
[tex]\dfrac{1}{16}+\cos^2 \theta =1[/tex]
[tex]\cos^2 \theta =1-\dfrac{1}{16}[/tex]
Taking square root on both sides.
[tex]\cos \theta =\pm \sqrt{\dfrac{16-1}{16}}[/tex]
[tex]\cos \theta =\pm \dfrac{\sqrt{15}}{4}[/tex]
Therefore, the value of cosθ is either [tex]\dfrac{\sqrt{15}}{4}[/tex] or [tex]-\dfrac{\sqrt{15}}{4}[/tex].
