How do you find the solution to $tan^2theta-3=0$ if $0<=theta<360$ ?

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How do you find the solution to $tan^2theta-3=0$ if $0<=theta<360$ ?

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Answer 1 · 2016-12-17T05:05:16

$theta=pi/3, (4pi)/3$

Explanation:

We have

$tan^2theta-3=0$

We can solve for $theta$ :

$tan^2theta=3$

$tantheta=sqrt3$

We can express $tan=sin/(cos)=sqrt3/1$

The triangle that has the ratio of $1, sqrt3,2$ is the 30-60-90 triangle. We have the opposite side as the medium length side, so we're talking about a reference angle of $60^o=pi/3$

Next thing to ask is where is tangent positive? Q1, Q3.

In Q1, we have $pi/3$

In Q3, we have $pi+pi/3=(4pi)/3$

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How do you find the solution to $tan^2theta-3=0$ if $0<=theta<360$ ?

1 Answer

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How do you find the solution to $tan^2theta-3=0$ if $0<=theta<360$ ?