How do you solve $sqrt(tanx)=root4(3)$ in the interval [0,360]?

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How do you solve $sqrt(tanx)=root4(3)$ in the interval [0,360]?

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Answer 1 · 2016-10-25T18:17:06

Rewrite both sides in radical form.

$(tanx)^(1/2) = 3^(1/4)$

We need to balance exponents.

$((tanx)^(1/2))^4 = (3^(1/4))^4$

$(tanx)^2 = 3$

$tan^2x = 3$

$tanx = +-sqrt(3)$

$x = 60^@, 120^@, 240^@, 300^@$

However, we can only take the solutions when the $sqrt(3)$ is positive, since the solutions located in quadrants where tangent is negative will render the original equation undefined.

So, $x = 60^@ and 240^@$

Hopefully this helps!

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How do you solve $sqrt(tanx)=root4(3)$ in the interval [0,360]?

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How do you solve sqrt(tanx)=root4(3)sqrt(tanx)=root4(3) in the interval [0,360]?

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How do you solve $sqrt(tanx)=root4(3)$ in the interval [0,360]?