- Demonstrate the ability to convert circles from rectangular form to polar form
- Demonstrate the ability to convert circles from polar form to rectangular form
- Demonstrate the ability to graph circles on the polar grid
#1:
Instructions: Convert each to polar form, then graph the polar equation.
$$a)\hspace{.1em}(x - 1)^2 + (y - 3)^2=10$$
$$b)\hspace{.1em}x^2 + (y - 3)^2=9$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: Convert each to polar form.
$$a)\hspace{.1em}(x + 2)^2 + (y + 2)^2=8$$
$$b)\hspace{.1em}(x - 2)^2 + (y + 1)^2=5$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: Convert each to rectangular form.
$$a)\hspace{.1em}r=4 \hspace{.1em}\text{cos}\left(θ + \frac{π}{3}\right) $$
$$b)\hspace{.1em}r=4 \hspace{.1em}\text{sin}\left(θ + \frac{π}{4}\right)$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: Convert each to rectangular form.
$$a)\hspace{.1em}r=4 \hspace{.1em}\text{cos}\left(θ + \frac{π}{6}\right)$$
$$b)\hspace{.1em}r=2 \hspace{.1em}\text{sin}\left(θ + \frac{π}{6}\right)$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: Convert each to rectangular form.
$$a)\hspace{.1em}r=2 \hspace{.1em}\text{cos}\left(θ + \frac{π}{4}\right)$$
$$b)\hspace{.1em}r=6 \hspace{.1em}\text{sin}\left(θ + \frac{π}{3}\right)$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}r=2 \hspace{.1em}\text{cos}\hspace{.1em}θ + 6 \hspace{.1em}\text{sin}\hspace{.1em}θ$$ 
$$b)\hspace{.1em}r=6 \hspace{.1em}\text{sin}\hspace{.1em}θ$$ 
Watch the Step by Step Video Solution
#2:
Solutions:
$$a)\hspace{.1em}r=-4 \hspace{.1em}\text{cos}\hspace{.1em}θ - 4 \hspace{.1em}\text{sin}\hspace{.1em}θ$$
$$b)\hspace{.1em}r=4 \hspace{.1em}\text{cos}\hspace{.1em}θ - 2 \hspace{.1em}\text{sin}\hspace{.1em}θ$$
Watch the Step by Step Video Solution
#3:
Solutions:
$$a)\hspace{.1em}(x - 1)^{2}+ (y + \sqrt{3})^{2}=4$$
$$b)\hspace{.1em}(x - \sqrt{2})^{2}+ (y - \sqrt{2})^{2}=4$$
Watch the Step by Step Video Solution
#4:
Solutions:
$$a)\hspace{.1em}(x - \sqrt{3})^{2}+ (y + 1)^{2}=4$$
$$b)\hspace{.1em}\left(x - \frac{1}{2}\right)^{2}+ \left(y - \frac{\sqrt{3}}{2}\right)^{2}=1$$
Watch the Step by Step Video Solution
#5:
Solutions:
$$a)\hspace{.1em}\left(x - \frac{\sqrt{2}}{2}\right)^{2}+ \left(y + \frac{\sqrt{2}}{2}\right)^{2}=1$$
$$b)\hspace{.1em}\left(x - \frac{3\sqrt{3}}{2}\right)^{2}+ \left(y - \frac{3}{2}\right)^{2}=9$$
