Convert the rectangular equation to polar form. Assume
$a 0$
$y = - 7$
A) $r = - \csc \theta$
B) $r = - 7 \sec \theta$
C) $r = - 7 \csc \theta$
D) $r = - 7 \cos \theta$
E) $r = - 7 \sin \theta$

Question

Convert the rectangular equation to polar form. Assume 
$a > 0$ 
$y = - 7$ 
A) $r = - \csc \theta$
B) $r = - 7 \sec \theta$
C) $r = - 7 \csc \theta$
D) $r = - 7 \cos \theta$
E) $r = - 7 \sin \theta$

Quizplus · Accepted Answer

For a point with rectangular coordinates $(x,y)$ and polar coordinates $(r,	heta)$, we have $r^2 = x^2 + y^2$ and $	an 	heta = \frac{y}{x}$. Since $y = -7$, we have $r^2 = x^2 + 49$. We can use the identity $\csc^2 	heta = 1 + \cot^2 	heta$ to write $r^2 = \frac{1}{\sin^2 	heta}$ as $r = -\csc 	heta$. Thus, the equation in polar form is $r = -7 \csc 	heta$.

Convert the Rectangular Equation to Polar Form a>0a > 0a>0 y=−7y = - 7y=−7

Convert the Rectangular Equation to Polar Form $a > 0$ $y = - 7$