Question

if sin theta =√3/2,cos theta=-1/2 then theta lies in​

Answer 1

SOLUTION

GIVEN

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

TO DETERMINE

θ lies in ______

EVALUATION

$\displaystyle \sf{ \sin \theta = \frac{ \sqrt{3} }{2} }$

Since sin θ is positive in first and second quadrant

∴ θ lies in first or second quadrant

$\displaystyle \sf{ \cos \theta = - \frac{1}{2} }$

Since cos θ is negative in second and third quadrant

∴ θ lies in second or third quadrant

Hence from above we can conclude that

θ lies in second quadrant

In particular θ = 120°

FINAL ANSWER

θ lies in second quadrant

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