Free Printable 8.3 Polar and Rectangular Forms of Equations

1.

Convert the rectangular equation to polar form.
$y=\frac{x}{2}$

a)

$\theta=\frac{5\pi}{6}$

b)

$\cot\theta=2$

c)

$\cot\theta=5$

d)

$\theta=\frac{3\pi}{4}$

2.

Convert the rectangular equation to polar form.
$y=-x\sqrt{3}$

a)

$\cot\theta=2$

b)

$\tan\theta=1$

c)

$\cot\theta=5$

d)

$\theta=\frac{2\pi}{3}$

3.

Convert the rectangular equation to polar form.
$\left(x-3\right)^2+y^2=9$

a)

$r=6\cos\theta$

b)

$r=-2\cos\theta+6\sin\theta$

c)

$r=6\cos\theta+2\sin\theta$

d)

$r=-6\sin\theta$

4.

Convert the rectangular equation to polar form.
$x^2+y^2=16$

a)

$r=4$

b)

$r=16$

c)

$r=4\cos\theta+4\sin\theta$

d)

$r=4\sin\theta$

5.

Convert the rectangular equation to polar form.
$x^2+\left(y-2\right)^2=4$

a)

$r=4\sin\theta$

b)

$r=6\sin\theta$

c)

$r=-2\cos\theta+4\sin\theta$

d)

$r=-4\cos\theta-2\sin\theta$

6.

Convert the rectangular equation to polar form.
$x^2+y^2=16$

a)

$r=4$

b)

$r=16$

c)

$r=4\cos\theta+4\sin\theta$

d)

$r=4\sin\theta$

7.

Convert the polar equation to rectangular form.
$\theta=\frac{5\pi}{6}$

a)

$y=-\frac{x\sqrt{3}}{3}$

b)

$y=\frac{x}{4}$

c)

$y=x$

d)

$y=-x\sqrt{3}$

8.

Convert the polar equation to rectangular form.
$r=2\tan\theta\sec\theta$

a)

$y=\frac{x^2}{2}$

b)

$x=y^2$

c)

$y=\frac{x^2}{4}$

d)

$x=\frac{y^2}{4}4$

9.

Convert the polar equation to rectangular form.
$\cot\theta=5$

a)

$y=\frac{x}{5}$

b)

$y=x\sqrt{3}$

c)

$y=x$

d)

$y=5x$

10.

Convert the polar equation to rectangular form.
$r=-4\sin\theta$

a)

$\left(x-2\right)^2+\left(y-1\right)^2=5$

b)

$\left(x-1\right)^2+\left(y-3\right)^2=10$

c)

$\left(x+1\right)^2+\left(y-2\right)^2=5$

d)

$x^2+\left(y+2\right)^2=4$

11.

Convert the polar equation to rectangular form.
$r=4\cos\theta-2\sin\theta$

a)

$\left(x+2\right)^2+y^2=4$

b)

$\left(x-2\right)^2+\left(y-1\right)^2=5$

c)

$\left(x-2\right)^2+\left(y+1\right)^2=5$

d)

$\left(x-1\right)^2+y^2=1$

12.

Find the polar coordinates of the rectangular point. (0,3)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

13.

Convert the rectangular coordinates to polar coordinates
(6√3, 6)

a)

(12, π/6)

b)

(6, 7π/6)

c)

(6, π/6)

d)

(12, 7π/6)

14.

How do you write an ordered pair in polar coordinates?

a)

(X, Y)

b)

(θ, r)

c)

(r,θ)

d)

(Y_Y)

15.

Convert the polar coordinates to rectangular form

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

16.

Convert the polar coordinates to rectangular form.
(6, 2π/3)

a)

( -3, 3)

b)

(3, 3√3)

c)

(-3, 3√3)

d)

(3, -3√3)

17.

Convert from polar to rectangular:

(5, 135^o)

a)

(-5√2/2, 5√2/2)

b)

(5√2/2, 5√2/2)

c)

(5√2/2, -5√2/2)

d)

(-5√2/2, -5√2/2)

18.

Convert the polar coordinates to rectangular coordinates.

a)

b)

c)

d)

19.

Find r
x=12
y=5

a)

12

b)

12.5

c)

13

d)

15

20.

Convert from rectangular to polar coordinates. (-4, 4)

a)

(4√2, π/4)

b)

(4√2, 3π/4)

c)

(4√2, -π/4)

d)

(-4√2, -7π/4)

8.3 Polar and Rectangular Forms of Equations

Total questions: 20

Worksheet time: 40mins

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