Find a polar equation for the parametric equations $x = 5 \cos ^ { 2 } \theta , y = 5 \cos \theta \sin \theta$
A) $x ^ { 2 } + y ^ { 2 } = 25 \cos ^ { 2 } \theta$
B) $r = 5 \cos \theta$
C) $r = 5 \sin \theta$
D) $y = x \tan \theta$

Question

Quizplus · Accepted Answer

To convert the given parametric equations to a polar equation, we use the relationships $x = r \cos \theta$ and $y = r \sin \theta$. Substituting $x = 5 \cos^2 \theta$ and $y = 5 \cos \theta \sin \theta$ into $r^2 = x^2 + y^2$, we get $r^2 = 25 \cos^2 \theta + 25 \cos^2 \theta \sin^2 \theta$. However, recognizing that $r = x/\cos \theta = 5 \cos \theta$ directly from $x = 5 \cos^2 \theta$ is a simpler and more direct approach, leading to the correct polar equation $r = 5 \cos \theta$.

Find a Polar Equation for the Parametric Equations x=5cos⁡2θ,y=5cos⁡θsin⁡θx = 5 \cos ^ { 2 } \theta , y = 5 \cos \theta \sin \thetax=5cos2θ,y=5cosθsinθ

Find a Polar Equation for the Parametric Equations $x = 5 \cos ^ { 2 } \theta , y = 5 \cos \theta \sin \theta$