- Demonstrate the ability to convert a line from rectangular form to polar form
- Demonstrate the ability to convert a line from polar form to rectangular form
- Demonstrate the ability to graph a line on the polar coordinate plane
#1:
Instructions: Convert to polar form, then graph on the polar grid.
$$a)\hspace{.1em}y=x$$
$$b)\hspace{.1em}y=\frac{x\sqrt{3}}{3}$$
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#2:
Instructions: Graph on the polar grid, then convert to rectangular form.
$$a)\hspace{.1em}r=-2\hspace{.1em}\text{csc}\left(θ + \frac{π}{4}\right)$$
$$b)\hspace{.1em}r=2\hspace{.1em}\text{csc}\left(θ + \frac{π}{6}\right)$$
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#3:
Instructions: Convert to rectangular form.
$$a)\hspace{.1em}r=\text{sec}\left(θ + \frac{π}{6}\right)$$
$$b)\hspace{.1em}r=4 \hspace{.1em}\text{sec}\left(θ + 45°\right)$$
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#4:
Instructions: Convert to rectangular form.
$$a)\hspace{.1em}r=3 \hspace{.1em}\text{sec}(θ + 60°)$$
$$b)\hspace{.1em}r=3 \hspace{.1em}\text{sec}\hspace{.1em}θ$$
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#5:
Instructions: Convert to rectangular form.
$$a)\hspace{.1em}r=4 \hspace{.1em}\text{csc}\hspace{.1em}θ$$
$$b)\hspace{.1em}r=\text{sec}(θ + 45°)$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.1em}θ=45° \text{or}\hspace{.25em}θ=225°$$
$$b)\hspace{.1em}θ=30° \text{or}\hspace{.25em}θ=210°$$
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#2:
Solutions:
$$a)\hspace{.1em}y=-x - 2\sqrt{2}$$
$$b)\hspace{.1em}y=-\frac{x\sqrt{3}}{3}+ \frac{4\sqrt{3}}{3}$$
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#3:
Solutions:
$$a)\hspace{.1em}y=x\sqrt{3}- 2$$
$$b)\hspace{.1em}y=x - 4\sqrt{2}$$
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#4:
Solutions:
$$a)\hspace{.1em}y=\frac{x\sqrt{3}}{3}- 2\sqrt{3}$$
$$b)\hspace{.1em}x=3$$
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#5:
Solutions:
$$a)\hspace{.1em}y=4$$
$$b)\hspace{.1em}y=x - \sqrt{2}$$
