Find the inclination (in degrees) of the line with a slope of m.Round your answer to one decimal places. $m = - 3$
A) $\Theta \approx 108.4 ^ { \circ }$
B) $\Theta \approx 109.4 ^ { \circ }$
C) $\Theta \approx 110.4 ^ { \circ }$
D) $\Theta \approx 107.4 ^ { \circ }$
E) $\Theta \approx 106.4 ^ { \circ }$

Question

Find the inclination  (in degrees) of the line with a slope of m.Round your answer to one decimal places.  $m = - 3$ 
A) $\Theta \approx 108.4 ^ { \circ }$
B) $\Theta \approx 109.4 ^ { \circ }$
C) $\Theta \approx 110.4 ^ { \circ }$
D) $\Theta \approx 107.4 ^ { \circ }$
E) $\Theta \approx 106.4 ^ { \circ }$

Quizplus · Accepted Answer

The inclination of a line with a slope of $m$ can be found using the formula $\Theta = \tan^{-1}(m)$. For $m = -3$, $\Theta = \tan^{-1}(-3)$. Since the tangent function is negative in the second and fourth quadrants, and the inclination is typically measured from the positive x-axis, we add $180^\circ$ to the result of $\tan^{-1}(-3)$ to get the angle in the correct quadrant. Thus, $\Theta \approx 180^\circ + \tan^{-1}(-3) \approx 180^\circ - 71.6^\circ = 108.4^\circ$.

Find the Inclination (In Degrees) of the Line with a Slope