Use the properties of inverse trigonometric functions to evaluate $\arctan \left[ \tan \left( \frac { 2 \pi } { 5 } \right) \right]$ .
A) $\frac { \pi } { 5 }$
B) $\frac { 2 \pi } { 3 }$
C) $\frac { 5 \pi } { 2 }$
D) $\frac { 2 \pi } { 5 }$
E) $- \frac { 3 \pi } { 5 }$

Question

Quizplus · Accepted Answer

The function $\arctan(\tan(x))$ simplifies to $x$ when $x$ is in the principal branch of $\arctan$, which is $-\frac{\pi}{2} < x < \frac{\pi}{2}$. However, since $\frac{2\pi}{5}$ is within the principal range of $\arctan$, the expression simplifies directly to $\frac{2\pi}{5}$.

Use the Properties of Inverse Trigonometric Functions to Evaluate arctan⁡[tan⁡(2π5)]\arctan \left[ \tan \left( \frac { 2 \pi } { 5 } \right) \right]arctan[tan(52π​)]

Use the Properties of Inverse Trigonometric Functions to Evaluate $\arctan \left[ \tan \left( \frac { 2 \pi } { 5 } \right) \right]$