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# Find$\sin \frac { \theta } { 2 } , \cos \frac { \theta } { 2 } , \text { and } \tan \frac { \theta } { 2 }$for the set of conditions.$\sin \theta = - \frac { 24 } { 25 } \text { and } 180 ^ { \circ } < \theta < 270 ^ { \circ }$

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

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

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

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

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

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

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

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

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

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