If ${\rm{sin \theta \;}} = - \frac{4}{{5\;}}$ and ${\rm{\theta \;}}$ lies in the third quadrant, then ${\rm{cos}}\,\,\frac{{\rm{\theta }}}{{2\;}}$ is equal to

JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

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Application +4 | -1

\mathrm{sin \theta \;} = - \frac{4}{{5\;}}

and

\mathrm{\theta \;}

lies in the third quadrant, then

\mathrm{cos}\,\,\frac{\mathrm{\theta }}{{2\;}}

is equal to

View answer and explanation

Correct option: B

- \frac{1}{{\sqrt 5 }}

Option B (-1/√5) is correct because, given sin θ is negative and θ is in the third quadrant, cos(θ/2) will be negative, and the calculation yields -1/√5.

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