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#?

1 Answer

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