# Question 0a9ed

Jun 4, 2017

$\theta = {102}^{\circ} \left(1.78 \text{rad}\right)$

and

$\theta = {282}^{\circ} \left(4.92 \text{rad}\right)$

The original condition repeats at any integer multiple of a full rotation of these angles.

#### Explanation:

According to reciprocal identities, $\tan \left(x\right) = \frac{1}{\cot} \left(x\right)$.
Therefore, $\cot \left(x\right) = - 0.2122$ is equal to $\tan \left(x\right) = \frac{1}{-} 0.2122$.

The tangent function is negative in the 2nd and 4th quadrant, and the inverse tangent function returns negative angles for negative values. To convert the negative angle into the two possible angles, we need to add ${180}^{\circ}$ and ${360}^{\circ}$, respectively:

$\theta = {180}^{\circ} + {\tan}^{-} 1 \left(\frac{1}{-} 0.2122\right)$

and

$\theta = {360}^{\circ} + {\tan}^{-} 1 \left(\frac{1}{-} 0.2122\right)$

theta = 180^@ - ~78^@

and

theta = 360^@ - ~78^@ #

$\theta = {102}^{\circ}$

and

$\theta = {282}^{\circ}$

The process is the same for radians but you add $\pi$ and $2 \pi$ respectively.

$\theta \approx 1.78$ and $\theta \approx 4.92$