Question

If sin theta = 1/4 and tan > 0 what is the value of cos theta

A. - square root of 15
B. square root of 15
C. square root of 15/4
D. - square root of 15/4

Answer 1

answer is letter C. See photo for solution

Answer 2

Option C.
`(1)/(4)√(15)`

Explanation:

It is given in the question

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

and we have to calculate the value of
`cos\theta`

since we know that

`cos\theta =\pm \sqrt{1-sin^(2)\theta }`

It has been given in the question that
`tan\theta >0` means sine and cosine both are of same sign so we will positive sign of cosine.

Now by putting the value of
`sin\theta` in the formula given

`cos\theta =\sqrt{1-sin^(2)\theta}=\sqrt{1-((1)/(4))^(2)}=\sqrt{(16-1)/(16)}=\sqrt{(15)/(16)}=(1)/(4)√(15)`

Therefore option C.
`(1)/(4)√(15)` is the answer.