Find the polar coordinates of the point(s) of intersection of the given curves for 0 $0 \leq \theta < 2 \pi$
- $r = 4 + \cos \theta , r = 4 - \sin \theta$

Question

Find the polar coordinates of the point(s) of intersection of the given curves for 0 $$0 \leq \theta < 2 \pi$$
-$r = 4 + \cos \theta , r = 4 - \sin \theta$
A) $\left( 4 , \frac { 3 \pi } { 4 } \right) , \left( 4 , \frac { 7 \pi } { 4 } \right)$

B) $\left( 4 - \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 4 + \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)$

C) $\left( 4 + \frac { 1 } { \sqrt { 2 } } , \frac { 3 \pi } { 4 } \right) , \left( 4 - \frac { 1 } { \sqrt { 2 } } , \frac { 7 \pi } { 4 } \right)$

D) $\left( \frac { 7 } { 2 } , \frac { 3 \pi } { 4 } \right) , \left( \frac { 9 } { 2 } , \frac { 7 \pi } { 4 } \right)$

Quizplus · Accepted Answer

To find the points of intersection, set $4 + \cos \theta = 4 - \sin \theta$. Solving gives $\cos \theta + \sin \theta = 0$, which implies $\theta = \frac{3\pi}{4}$ and $\theta = \frac{7\pi}{4}$. Substituting these values into either equation gives the corresponding $r$ values.

Find the Polar Coordinates of the Point(s) of Intersection of the Given