Mathematics: Why are there two values of theta if tan theta = 0.4226

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Why are there two values of theta if tan theta =

kyleeeeee94

06.02.2022

$22.91^\circ, 202.91^\circ$

Step-by-step explanation:

Given that:

$tan\theta=0.4226$

To find:

The two values of $\theta = ?$

Solution:

By given equation:

$\theta = tan^{-1}(0.4226)$

$\theta$ can be equal to $\approx 20.91^\circ$

Also, we know the property that, $tan\theta$ is positive in the 3rd quadrant.

and following is also true:

$tan\theta = tan(180^\circ+\theta)$

Therefore, another value possible for $\theta$ can be:

$\theta =180^\circ+22.91\\\Rightarrow \theta \approx 202.91^\circ$

Therefore, the answer is:

$22.91^\circ, 202.91^\circ$

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