Question

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

Answer 1

Answer is letter C. See photo for solution

Answer 2

Answer:

Option C. $\frac{1}{4}\sqrt{15}$

Step-by-step explanation:

It is given in the question

$sin\theta =\frac{1}{4}$

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

$cos\theta =\sqrt{1-sin^{2}\theta}=\sqrt{1-(\frac{1}{4})^{2}}=\sqrt{\frac{16-1}{16}}=\sqrt{\frac{15}{16}}=\frac{1}{4}\sqrt{15}$

Therefore option C. $\frac{1}{4}\sqrt{15}$ is the answer.