Question 1061978
.
If sin theta = -5/13 and theta terminates in 3rd quadrant find cos theta and tan theta.
~~~~~~~~~~~~~~~~~


<pre>
In QIII  {{{cos(theta)}}} = {{{-sqrt(1-sin^2(theta))}}} = {{{-sqrt(1-(-5/13)^2)}}} = {{{-sqrt(1-25/169)}}} = {{{-sqrt((169-25)/169)}}} = {{{-sqrt(144/169)}}} = {{{-12/13}}}.


Then   {{{tan(theta)}}} = {{{sin(theta)/cos(theta))}}} = {{{((-5/13))/((-12/13))}}} = {{{5/12}}}.
</pre>

Solved.