Can you show me how to find the rectangular equation:
r=2cos(theta) + 3 sin (theta)
All I need is an example to work off I was absent today from Pre-Calc and I have homework to do and no explanation with them-Please help with this one Thank you
sqrt(x^2+y^2) = 2 x/sqrt(x^2+y^2)+3y/sqrt(x^2+y^2)
x^2+y^2 = 2 x + 3 y
y^2 - 3 y = -x^2 + 2 x
Thank you
Certainly! To find the rectangular equation for the given equation, we can use the following trigonometric identities:
1. cos(theta) = x / r, where x represents the x-coordinate.
2. sin(theta) = y / r, where y represents the y-coordinate.
Now, we can rewrite the given equation:
r = 2cos(theta) + 3sin(theta)
Substituting the values from the trigonometric identities, we have:
r = 2(x / r) + 3(y / r)
Multiplying both sides of the equation by r, we get:
r^2 = 2x + 3y
Now we need to substitute the value of r^2 with the corresponding Cartesian coordinates using the Pythagorean identity:
r^2 = x^2 + y^2
Replacing r^2 with x^2 + y^2 in the previous equation, we have:
x^2 + y^2 = 2x + 3y
Rearranging the equation, we get:
x^2 - 2x + y^2 - 3y = 0
Finally, we can simplify this equation, which is the rectangular equation of the given polar equation:
x^2 - 2x + y^2 - 3y = 0
Now you can use this equation to complete your homework.