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