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

Using the property of inverse tangent function, we have:

tan(11ea99db_b4c9_9ac7_94ac_6fc27c55a56a_TB4590_00) = - sqrt(3)/3

Taking the arctangent of both sides:

11ea99db_b4c9_9ac7_94ac_6fc27c55a56a = atan(-sqrt(3)/3)

Using the property of inverse cosine function, we have:

cos(11ea99db_b4c9_e8eb_94ac_cd18dd3de1fd_TB4590_11) = - sqrt(3)/2

Taking the arccosine of both sides:

11ea99db_b4c9_e8eb_94ac_cd18dd3de1fd = arccos(-sqrt(3)/2)

Therefore, the best choice is (D).

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 $\arctan \left[ \tan \left( \frac { 2 \pi } { 5 } \right) \right]$