Find Three Additional Polar Representations of the Point $\left( 5 , - \frac { \pi } { 3 } \right)$

question 13

Multiple Choice

Find three additional polar representations of the point $\left( 5 , - \frac { \pi } { 3 } \right)$ , given in polar coordinates, using $- 2 \pi < \theta < 2 \pi$ .

• A) \(\left( 5 , \frac { 5 \pi } { 3 } \right) , \left( 5 , \frac { 2 \pi } { 3 } \right) , \left( - 5 , - \frac { 4 \pi } { 3 } \right)\)
• B) \(\left( 5 , \frac { 5 \pi } { 3 } \right) , \left( 5 , \frac { 2 \pi } { 3 } \right) , \left( 5 , - \frac { 4 \pi } { 3 } \right)\)
• C) \(\left( 5 , \frac { 5 \pi } { 3 } \right) , \left( - 5 , \frac { 2 \pi } { 3 } \right) , \left( - 5 , - \frac { 4 \pi } { 3 } \right)\)
• D) \(\left( - 5 , \frac { 5 \pi } { 3 } \right) , \left( - 5 , \frac { 2 \pi } { 3 } \right) , \left( 5 , - \frac { 4 \pi } { 3 } \right)\)
• E) \(\left( - 5 , \frac { 5 \pi } { 3 } \right) , \left( 5 , \frac { 2 \pi } { 3 } \right) , \left( - 5 , - \frac { 4 \pi } { 3 } \right)\)