Question 1056289
.
if cosx=-12/13 and sin x>0, find tan(2x)
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<pre>
0.  The useful notice is: Since cos(x) is negative and sin(x) is positive, the angle "x" terminates in QII.


1.  Since cos(x) = {{{-12/13}}}, sin(x) = {{{sqrt(1-cos^2(x))}}} = {{{sqrt(1-(-12/13)^2)}}} = {{{sqrt(1-144/169)}}} = {{{sqrt((169-144)/169)}}} = {{{sqrt(25/169)}}} = {{{5/13}}}.

    The sign is "+" at the square root, since sine is positive, according to the condition.


2.  Then {{{tan(x)}}} = {{{sin(x)/cos(x)}}} = {{{((5/13))/((-12/13))}}} = {{{-5/12}}}.


3.  Finally, {{{tan(2x)}}} = {{{(2*tan(x))/(1-tan^2(x))}}} = {{{(2*(-5/12))/(1-((-5/12)^2))}}} = {{{((-10/12))/((1-25/144))}}} = {{{((-10/12))/(((144-25)/144))}}} = {{{((-10/12))/((119/144))}}} = {{{(-10*144)/(12*119)}}} = {{{(-10*12)/119}}} = {{{-120/119}}}.
</pre>

Solved.


For more solved similar problems on calculating trig functions 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>".