Question

tan theta is equal to 1 by root 3 and Cos theta is equal to root 3 by 2 then find sin theta​

Answer 1

SOLUTION

GIVEN

$\displaystyle\sf{ \tan \theta = \frac{1}{ \sqrt{3} } \: \: and \: \: \cos \theta = \frac{ \sqrt{3} }{2} }$

TO DETERMINE

The value of

$\displaystyle\sf{ \sin \theta }$

EVALUATION

Here it is given that

$\displaystyle\sf{ \tan \theta = \frac{1}{ \sqrt{3} } \: \: and \: \: \cos \theta = \frac{ \sqrt{3} }{2} }$

So tan θ and cos θ are both positive

Thus θ lies in first quadrant

$\displaystyle\sf{ \tan \theta = \tan {30}^{ \circ} \: \: and \: \: \cos \theta = \cos {30}^{ \circ} }$

$\displaystyle\sf{ \implies \theta = {30}^{ \circ} }$

Therefore

$\displaystyle\sf{ \sin \theta }$

$\displaystyle\sf{ = \sin {30}^{ \circ} }$

$\displaystyle\sf{ = \frac{1}{2} }$

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