Question 1061183
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determine the exact value of sin2ø given that cosø=-12/13 and &#960;<ø<3&#960;/2 without determine the value of ø.
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<pre>
If  {{{cos(phi)}}} = {{{-12/13}}} and {{{pi}}} < {{{phi}}} <= {{{3pi/2}}}, then

{{{sin(phi)}}} = {{{-sqrt(1-sin^2(theta))}}} = {{{-sqrt(1-(-12/13)^2)}}} = {{{-sqrt(1-144/169)}}} = {{{-sqrt((169-144)/169)}}} = {{{-sqrt(25/169)}}} = {{{-5/13)}}}.

The sign  "-"  was taken at  sqrt,  because sine is negative in QIII.


Then 

{{{cos(2*phi)}}} = {{{2*sin(phi)*cos(phi)}}} = {{{2*(-5/13)*(-12/13)}}} = {{{120/169}}}.
</pre>

Solved.



For many other similar solved 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.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Trigonometry: Solved problems</U>".