How do you find all solutions if 0 ≤ θ < 2π for $tan 2theta = sqrt3$ ?

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How do you find all solutions if 0 ≤ θ < 2π for $tan 2theta = sqrt3$ ?

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Answer 1 · 2016-02-18T10:45:35

General solution is $(npi+pi/6)$ , where $n$ is an integer.

Explanation:

Note that $tan2theta=sqrt3$ . As it is positive, it can lie either in 1st or 3rd quadrant. As $tan(pi/3)=sqrt3$ , $2theta=pi/3$ or $theta=pi/6$ . In 3rd quadrant it will be $pi+pi/6$ .

We can also have solutions by adding / subtracting $2pi$ to these solutions.

Hence, general solution is $(npi+pi/6)$ , where $n$ is an integer.

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How do you find all solutions if 0 ≤ θ < 2π for $tan 2theta = sqrt3$ ?

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How do you find all solutions if 0 ≤ θ < 2π for tan 2theta = sqrt3tan 2theta = sqrt3?

1 Answer

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How do you find all solutions if 0 ≤ θ < 2π for $tan 2theta = sqrt3$ ?