Find all angles θ between 0° and 180° satisfying the given equation tan(θ) = −24

Answer 1

The angle θ is the inverse of the tan^-1 tan ( θ) = tan^-1 ( -24) = - 87.6^ο

This angle occurs in the third quadrant of the unit circle

The angle required is between 0^ο and 180^ο , and the -87.6^ο does not occur in the interval or in the first and 2nd quadrant. Therefore, there is no angle that satisfies the equation above in the interval.