# 1. Find the corresponding rectangular coordinates for the polar point (-2, 7pi/6) 2. Convert...

## Question:

1. Find the corresponding rectangular coordinates for the polar point {eq}\displaystyle (-2,\frac{7\pi }{6}) {/eq}

2. Convert the rectangular equation {eq}\displaystyle x^{2}+y^{2}-2y=0 {/eq} to polar form,

a) {eq}\displaystyle r=2\cos \theta {/eq}

b) {eq}\displaystyle r=\frac{1}{2}\csc \theta {/eq}

c) {eq}\displaystyle r=2\sin \theta {/eq}

d) {eq}\displaystyle r=-2\sin \theta {/eq}

e) None of the above

3. Convert the rectangular equation {eq}\displaystyle x^{2}=3y {/eq} to polar form.

a) {eq}\displaystyle r=3\sin \theta -\cos ^{2}\theta {/eq}

b) {eq}\displaystyle r=3\sec \theta \tan \theta {/eq}

c) {eq}\displaystyle r=3\csc \theta \cot \theta {/eq}

d) {eq}\displaystyle r=3\cos \theta -\sin ^{2}\theta {/eq}

e) None of the above.

## Polar Coordinates

To convert rectangular equations {eq}\displaystyle f(x,y)=0 {/eq} into polar coordinates {eq}\displaystyle g(r,\theta)=0 {/eq} we will use the following rectangular-polar conversion {eq}\displaystyle x=r\cos \theta, y=r\sin \theta. {/eq}

To obtain a polar point when the rectangular coordinates are given, we should keep in mind that the polar form is not unique,

because we can read the polar angle clockwise or counterclockwise or the polar radius, positive or negative,

therefore it may be up to four polar forms corresponding to a unique Cartesian form.