Question

solve cotθ = square root of 3 for θ

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

\[\cot \theta=\sqrt{3}\]
\[\frac{1}{\tan \theta}=\sqrt{3}\]
\[\tan \theta=\frac{1}{\sqrt{3}}\]
now let's think when we go around the unit circle will
\[\frac{\sin \theta}{\cos \theta}=\frac{1}{\sqrt3}\]
how about what happens at pi/6
\[\sin \frac{\pi}{6}=\frac{\sqrt{3}}{2}, \cos \frac{\pi}{6}=\frac{1}{2}\]
pi/6 will not wotk since tanpi/6 will not give us 1/sqrt{3}
so the answer is pi/3

Answer 3

but this repeats it self as we go around the circle some more

Answer 4

cosx/sinx =root(3), so cosx = sinx * root(3), lets square both sides cos²x = 3sin²x, then sin²x = 1 - cos²x, so cos²x = 3(1-cos²x), so cos²x = 3-3cos²x, so 4cos²x = 3, then cosx = root(3)/2, special triangles and that is x = pi/3.

Answer 5

Maniniya is right, but that answer is derived from intuition where as mine is a systematic process, hope that helps :)

Answer 6

thank you very much.

Answer 7

Np, i wouldn't mind getting a life saver :P

Answer 8

this is my first time posting a question. how do I give those?

Answer 9

or the "good answer" button?

Answer 10

we also have x=7pi/6
so all the answers are
x=pi/3+2npi
x=7pi/6+2npi
for n=0,1,2,3,4,...

Answer 11

I think u click on the user name and then click life saver

Answer 12

you can become a fan of his by clicking his name
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you can click good answer to give him a medal
or
you can do both

Answer 13

where did you get "pi/6"?