Choose the one alternative that best completes the statement or answers the question.
-If $\tan \theta = - 4.5$, find the value of $\tan \theta + \tan ( \theta + \pi ) + \tan ( \theta + 2 \pi )$.
A) $- 11.5$
B) $- 13.5 + 3 \pi$
C) $- 13.5$
D) undefined

Question

Quizplus · Accepted Answer

The tangent function has a period of $\pi$, meaning $\tan(\theta) = \tan(\theta + \pi) = \tan(\theta + 2\pi)$. Therefore, if $\tan(\theta) = -4.5$, then $\tan(\theta) + \tan(\theta + \pi) + \tan(\theta + 2\pi) = -4.5 + (-4.5) + (-4.5) = -13.5$.

Choose the One Alternative That Best Completes the Statement or Answers