Question

evaluate without a calculator:
cot(tan^-1 (1/2))

Answer 1

first evaluate tan^-1(1/2)

to evaluate an inverse trig function like this you ask yourself, the tangent of what is equal to 1/2?

Answer 2

so tan(x) = 1/2

Answer 3

yes

Answer 4

how do i find that?

Answer 5

if you notice, you see you'll have to find the value of cosx

Answer 6

ok, so sin(x) = sqrt of 3/1

Answer 7

nopes..recheck..

Answer 8

cos (x) = sqrt 3 / 2

Answer 9

sqrt 5

Answer 10

yes,,it'll be sqrt 5..

now cosx = 2/sqrt5
and hence your ans.

Answer 11

of the whole thing?

Answer 12

Remember, cotangent is Adjacent/Opposite while tangent is Opposite/Adjacent. By doing one and then the other, you're really just flip-flopping the fraction! No need to get crazy here with the math.

Answer 13

oh yea... dur

check this out

\[ \tan^{-1} (\sqrt{3}) = \pi / 3\]

\[\cot(\pi / 3) = \frac{ 1 }{ \sqrt{3} }\]

just flipped it... thanks Kainui!

Answer 14

Another way to look at it is that cot(x)=1/tan(x) so you can really just say this problem is doing:

\[\frac{ 1 }{ \tan(\tan^{-1}(x)) }\]

Answer 15

So yeah, you don't really have to plug this one into a calculator lol.