Question

Find the exact value of cotan(\sqrt{3})
I know how to compute exact values for the primary trig ratios, but how do you do so with their inverses?

Answer 1

do you mean arctan(sqrt(3))?

Answer 2

Yes

Answer 3

I don't want the answer, rather I want to know what method we use to get it.

Answer 4

Well remember sin(pi/3) = sqrt(3)/2 and cos(pi/3) = 1/2, hence ...

Answer 5

What method we use to find it, and for any other inverse trig ratios, how would I get the exact value?

Answer 6

In this case you should just learn the value of sin, cos and tan for all these angles
x = 0, pi/6, pi/4, pi/3, pi/2

Answer 7

and then you'll know this one.

Answer 8

these and all the variations (pi/2 - x), (x + pi), etc. will then be available to you.

Otherwise, frankly you're estimating. There are numerical methods to find arctan(a) for a given a.

Answer 9

I don't get it. How would that help me get the inverse values?

Answer 10

So for this, the answer is pi/6?

Answer 11

Well, if you know cos(pi/4) = 1/sqrt(2) for instance, then you know that for the standard range of arccos,
arccos(1/sqrt(2)) = pi/4

Answer 12

Hence, for example, what is arctan(1)?

Answer 13

sorry, you are calculating arctan(sqrt(3))

Answer 14

then the answer is not pi/6.