Solve the problem.
-If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 4$, find the exact value of $f ( a ) + f ( a + \pi ) + f ( a + 3 \pi )$.
A) $- 4$
B) $- 12 + 4 \pi$
C) $- 12$
D) undefined

Question

Quizplus · Accepted Answer

The cotangent function, $\cot \theta$, has a period of $\pi$, meaning $\cot(\theta + \pi) = \cot \theta$. Given $f(a) = \cot a = -4$, then $f(a + \pi) = \cot(a + \pi) = \cot a = -4$ and $f(a + 3\pi) = \cot(a + 3\pi) = \cot a = -4$. Adding these values, $f(a) + f(a + \pi) + f(a + 3\pi) = -4 - 4 - 4 = -12$.

Solve the Problem f(θ)=cot⁡θf ( \theta ) = \cot \thetaf(θ)=cotθ And f(a)=−4f ( a ) = - 4f(a)=−4

Solve the Problem $f ( \theta ) = \cot \theta$ And $f ( a ) = - 4$