Precalculus : Polar Coordinates and Complex Numbers

Example Questions

Example Question #1 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert from polar form to rectangular form:

Explanation:

Start by multiplying both sides by .

Keep in mind that

Remember that

So then,

Now, complete the square.

Example Question #2 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

Explanation:

Start by multiplying both sides by .

Remember that

Keep in mind that

So then,

Now, complete the square.

This is a graph of a circle with a radius of  and a center at

Example Question #3 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

Explanation:

Remember that

So then  becomes

Now, multiply both sides by  to get rid of the fraction.

Since  the rectangular form of this equation is

Example Question #4 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

Explanation:

Start by using the double angle formula for .

Substitute that into the equation gives the following:

Because we need  and  to get  and  respectively, multiply both sides by .

Now, recall that .

Example Question #5 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

Explanation:

Start by taking the tangent.

Recall that

Example Question #6 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

Explanation:

Start by taking the tangent.

Recall that

Example Question #7 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation to rectangular form:

Explanation:

Recall that

Substituting this into the given equation gives

Multiply both sides by  to get rid of the fraction.

Recall that  and that

Example Question #8 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

Explanation:

Recall that  and

Multiply both sides by

Recall that  and

Example Question #9 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form:

Explanation:

Recall that

Plugging this into the equation gives us

Multiply both sides by  to get rid of the fraction.

Recall that

So then the rectangular form of the equation is

Example Question #10 : Convert Polar Equations To Rectangular Form And Vice Versa

Convert the polar equation into rectangular form.

Explanation:

Recall that

Multiply both sides by  to get rid of the fraction.

Recall that .