# How do you convert the following to a rectangular equation: #r = cos (theta) - sin (theta)#?

##### 2 Answers

#### Explanation:

When converting from polar to rectangular equations you have to switch the references to

Multiply each term by

Simply

Make the necessary substitutions

Gather the

Now complete the square. Take the coefficient of both the

Insert the above 2 quantities on both sides of the equation to keep it balanced.

Simplify

Convert the 2 perfect square trinomials

Check out this tutorial on the conversion of equations from polar to rectangular.

Check out this tutorial on completing the square graphically

Check out this tutorial on completing the square analytically.

representing the circle through the origin,

with center at

#### Explanation:

Use the conversion equation

gives

Here,

Cross multiplying,

with center at

Noe that the general polar equation of the circles through the pole r

= 0 is