Question 1037376
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Given {{{cos(theta)}}} = -{{{7/25}}} and 180° < {{{theta}}} < 270°; find the exact value of {{{sin(theta/2)}}}.
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<pre>
Use the formula of Trigonometry

{{{sin^2(theta/2)}}} = {{{(1-cos(theta))/2}}}

(se the lesson <A HREF=>Trigonometric functions of half argument</A> in this site).

You will have

{{{sin(theta/2)}}} = {{{sqrt((1-(-7/25)^2)/2)}}} = {{{sqrt((1 - 49/625)/2)}}} = {{{sqrt((625-49)/(2*625))}}} = {{{sqrt(576/(2*625))}}} = {{{24/(sqrt(2)*25)}}} = {{{(12*sqrt(2))/25}}}.

The sign "+" was chosen at the square root since the angle {{{theta/2}}} lies in the 2-nd quadrant.
</pre>

For similar problems see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Calculating-trigonometric-functions-of-angles.lesson>Calculating trigonometric functions of angles</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Selected-problems-from-the-archive-on-calculating-trig-functions-of-angles.lesson>Advanced problems on calculating trigonometric functions of angles</A>

in this site.