## Related questions with answers

Find

$\sin \frac { \theta } { 2 } , \cos \frac { \theta } { 2 } , \text { and } \tan \frac { \theta } { 2 }$

for the set of conditions.

$\sin \theta = - \frac { 24 } { 25 } \text { and } 180 ^ { \circ } < \theta < 270 ^ { \circ }$

Solution

Verified$\text{\color{#c34632}Since $180\text{\textdegree}<\theta<270\text{\textdegree}$, we can write $\cos\theta = -\sqrt{1-\sin^2\theta}$}$

$\cos\theta = -\sqrt{1-\left( -\dfrac{24}{25}\right)^2}$

$\cos\theta = -\sqrt{1-\dfrac{24^2}{25^2}}$

$\cos\theta = -\sqrt{\dfrac{25^2-24^2}{25^2}}$

$\cos\theta = -\sqrt{\dfrac{\left( 25-24\right)\left(25+24 \right)}{25^2}}$

$\cos\theta = -\sqrt{\dfrac{\left( 1\right)\left(49 \right)}{25^2}}$

$\cos\theta = -\sqrt{\dfrac{49}{25^2}}$

$\cos\theta = -\dfrac{\sqrt{49}}{\sqrt{25^2}}$

$\cos\theta = -\dfrac{7}{25}$

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