Question

cot 5pi/6

Answer 1

You could find the tangent and change it to its reciprocal.

Answer 2

\[\cot \frac{ 5\pi }{6 }=\cot \left( \pi-\frac{ \pi }{6 } \right)=-\cot \frac{ \pi }{6 }=-\frac{ \frac{ \sqrt{3} }{2 } }{\frac{ 1 }{ 2 }}=-\sqrt{3}\]

Answer 3

For the purposes of highschool maths (or in most other situations) you can use your calculator to work this out.
Knowing that cotx = 1/tanx and tanx = 1/cotx, you can type into your calculator
1/tan(5pi/6) and press =, making sure your calculator is in radians mode.
You should end up with a strange decimal answer, but that's ok!
Note down whether or not the answer is negative, then square the answer. Your calculator should give you a whole number or fraction and your answer should be the square root of that.
For example, say we have cos(3pi/4). If we put that into our calculator (making sure it's in radians mode!) we should get something like -0.7071067... which means nothing to us. However, we know that the answer is going to be negative, as it gave us a negative sign. Now, if we square the answer we should get 0.5, or 1/2. If you take the square root of that, you'd get \[\frac{ \sqrt{1} }{ \sqrt{2}}\] which means that your final answer should be simplified as \[\frac{ -1 }{ \sqrt{2}}\]
Try using a similar approach for your own question and see what you get.