Question

Find tan theta if cos theta=1/4 and falls in quadrant one?

Answer 1

`\tan\theta=√(15)`

Explanation:

In quadrant I, all the trigonometric ratios are positive.

It was given that;

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

`\implies \sec\theta=4`

We use the Pythagorean identity;

`\sec^2\theta=1+tan^2\theta`

`4^2=1+tan^2\theta`

`16-1=tan^2\theta`

`15=tan^2\theta`

`\tan\theta=\pm√(15)`

since we are in the first quadrant;
`\tan\theta=√(15)`