Question

Find all angles $\theta$ between $0°$ and $180°$ satisfying the given equation.

Round your answer to one decimal place. (enter your answers as a comma-separated list.)

$\tan \left(\theta \right)=-21$

Answer 1

Compute the value of the angle:

Given that $\tan \left(\theta \right)=-21$.

Use the inverse function and write the angle as $\theta ={\tan }^{-1}(-21)$.

Use the calculator to obtain the value of ${\tan }^{-1}(-21)$.

${\tan }^{-1}(-21)=-87.3°$

Since angle must lie between $0°$ and $180°$.

It implies that the angle should be present in the first or second quadrant.

As $\tan \left(\theta \right)=-21$ means angle will be in the second quadrant.

Add $180°$ to $-87.3°$ to obtain the angle which lies in the second quadrant.

$\theta =-87.3°+180°$

$\therefore \theta =92.7°$

Hence, the required angle is $92.7°$.