Question 1198721
<font color=black size=3>
cos(theta) < 0 and tan(theta) < 0 are two given pieces of information. 
This narrows theta to quadrant Q2 in the northwest corner.


cos(theta) = adjacent/hypotenuse = -1/5
adjacent = -1
hypotenuse = 5


Use the pythagorean theorem to find the opposite side is {{{2*sqrt(6)}}}, which is equivalent to {{{sqrt(24)}}}, but I'll stick with the first version I mentioned.


Diagram:
*[illustration Screenshot_170.png]
adjacent = -1
hypotenuse = 5
opposite = {{{2*sqrt(6)}}}


The adjacent value is negative since we're in negative x coordinate territory.


Relevant formulas
cot(theta) = adjacent/opposite
sin(theta) = opposite/hypotenuse


I'll let you finish up.


A similar question is found here:
<a href = "https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1198723.html">https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1198723.html</a>
</font>