Question 1189410
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If sin theta=5/12, determine sin2theta, where theta is in the first quadrant.
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<pre>
Use the basic formula of Trigonometry

    {{{sin(2theta)}}} = {{{2sin(theta)*cos(theta)}}}.


From this formula, you see that you need to know {{{cos(theta)}}}.


It is easy to calculate  {{{cos(theta)}}}  from  {{{sin(theta)}}}

    {{{cos(theta)}}} = {{{sqrt(1-sin^2(theta))}}} = {{{sqrt(1 - (5/12)^2)}}} = {{{sqrt(1-25/144)}}} = {{{sqrt((144-25)/144)}}} = {{{sqrt(119/144)}}} = {{{sqrt(119)/12}}}.


In the first quadrant, cosine is positive; therefore, we keep the positive sign of the square root.


Now  {{{sin(2theta)}}} = {{{2sin(theta)*cos(theta)}}} = {{{2*(5/12)*(sqrt(119)/12)}}} = {{{(10/144)*sqrt(119)}}} = 0.757549...   <U>ANSWER</U>
</pre>

Solved.


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P.S.  &nbsp;&nbsp;My inner voice tells me that should be &nbsp;&nbsp;{{{sin(theta)}}} = {{{5/13}}}  &nbsp;&nbsp;in your post, &nbsp;instead of &nbsp;{{{5/12}}}.


If it is so, &nbsp;do everything the same. &nbsp;In this case the answer is  &nbsp;&nbsp;{{{sin(2theta)}}} = {{{2*(5/13)*(12/13)}}} = {{{120/169}}}.