Answer:
Option C. [tex]\frac{1}{4}\sqrt{15}[/tex]
Step-by-step explanation:
It is given in the question
[tex]sin\theta =\frac{1}{4}[/tex]
and we have to calculate the value of [tex]cos\theta[/tex]
since we know that
[tex]cos\theta =\pm \sqrt{1-sin^{2}\theta }[/tex]
It has been given in the question that [tex]tan\theta >0[/tex] means sine and cosine both are of same sign so we will positive sign of cosine.
Now by putting the value of [tex]sin\theta[/tex] in the formula given
[tex]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}[/tex]
Therefore option C. [tex]\frac{1}{4}\sqrt{15}[/tex] is the answer.
