How do you solve the equation 3sqrt3tanu=3?

1 Answer
Radioactive Teddybear
Apr 7, 2017

u=pi/6+2pix
u=(7pi)/6+2pix
x is an integer

Explanation:

Some concepts needed when finding u:
(x,y)=(cos,sin)
tan=sin/cos

Math:
3sqrt"3"tanu=3
tanu=3/(3sqrt3)
tanu=1/sqrt3
u=tan^-1(1/sqrt3) and tan^-1((-1)/-sqrt3)=pi/6 and (7pi)/6
Unit CircleUnit Circle
This is because the ratio which fits one over square root of three is one half over two divided by square root of three since the twos cancel out. Negatives also cancel, which is why there are 2 answers.

In reality, there would be an infinite amount of solutions with equations since angles can keep going around. So since a full rotation is 2pi, you can model the equation like
u=pi/6+2pix and u=(7pi)/6+2pix where x is an integer

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