Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. $\left( 8 , \frac { 7 \pi } { 5 } \right)$
A)Rectangular coordinates: (7.61,0.07)
B)Rectangular coordinates: (7.61,-7.61)
C)Rectangular coordinates: (-2.47,-7.61)
D)Rectangular coordinates: (-2.47,7.61)
E)Rectangular coordinates: (-2.47,0.07)

Question

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.  $\left( 8 , \frac { 7 \pi } { 5 } \right)$ 
A)Rectangular coordinates: (7.61,0.07)
B)Rectangular coordinates: (7.61,-7.61)
C)Rectangular coordinates: (-2.47,-7.61)
D)Rectangular coordinates: (-2.47,7.61)
E)Rectangular coordinates: (-2.47,0.07)

Quizplus · Accepted Answer

To convert from polar coordinates $(r, \theta)$ to rectangular coordinates $(x, y)$, we use the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$. For the given polar coordinates $\left( 8 , \frac { 7 \pi } { 5 } \right)$, we calculate:- $x = 8 \cos\left(\frac{7\pi}{5}\right) \approx -2.47$- $y = 8 \sin\left(\frac{7\pi}{5}\right) \approx -7.61$Therefore, the rectangular coordinates are approximately $(-2.47, -7.61)$.

Find the Rectangular Coordinates of the Point Given in Polar (8,7π5)\left( 8 , \frac { 7 \pi } { 5 } \right)(8,57π​)

Find the Rectangular Coordinates of the Point Given in Polar $\left( 8 , \frac { 7 \pi } { 5 } \right)$