Question

cot (5pi) step by step

Answer 1

You need to know that all values of cosine from 0-2pi would repeat, as cosine is a periodic function. All values after 2pi will be the same as you are only giving a turn to a circle and you are starting again and again after you reach 2pi . Knowing this, you can notice cos(5pi)=cos(pi)=0I will try to explain this with a drawing. Remember pi=180º
This is the first turn to the circle, the second turn would be like this
The circle ends with 2pi, and every time you give a half turn to it you add 180º=pi.
Now showing the 3rd turn to the circle:

As you may notice, 5pi has the same position as pi.Which means that the value of cosine would be the same. No matter how many turns you did.