Question

if sin a =1/4 evaluate cos a and tan a​

Answer 1

Step-by-step explanation:

We have,,

$\sf{\sin(A) = \frac{1}{4}}$

$\sf{\implies{\sin^{2}(A )= \frac{1}{16}}}$

$\sf{\implies{1-\cos^{2}(A) = \frac{1}{16}}}$

$\sf{\implies{\cos^{2}(A) =1- \frac{1}{16}}}$

$\sf{\implies{\cos^{2}(A )= \frac{16-1}{16}}}$

$\sf{\implies{\cos^{2}(A )= \frac{15}{16}}}$

$\sf{\implies{\cos(A) = \sqrt{\frac{15}{16}}}}$

$\sf{\implies{\boxed{\sf{\cos(A) = \frac{\sqrt{15}}{4}}}}}$

$\sf{\implies{\tan(A)=\frac{\sin(A)}{\cos(A)}= \frac{\frac{1}{4}}{\frac{\sqrt{15}}{4}}}}$

$\sf{\implies{\boxed{\sf{\tan(A)=\frac{1}{\sqrt{15}}}}}}$

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