change the equation to rectangular coordinates: r= 2(sin theta -cos theta)
Ok, Meredith, after doing this one for you
http://www.jiskha.com/display.cgi?id=1482199382
surely you can follow the same steps for this one.
To convert the equation from polar coordinates to rectangular coordinates, we can use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
In this case, the given equation is r = 2(sin(theta) - cos(theta)).
Let's convert it step-by-step:
Step 1: Expand the equation:
r = 2sin(theta) - 2cos(theta)
Step 2: Convert r to x and y:
x = (2sin(theta) - 2cos(theta)) * cos(theta)
y = (2sin(theta) - 2cos(theta)) * sin(theta)
So, the rectangular coordinates of the given equation in terms of x and y are:
x = (2sin(theta) - 2cos(theta)) * cos(theta)
y = (2sin(theta) - 2cos(theta)) * sin(theta)
To change the equation from polar coordinates to rectangular coordinates, we can use the following conversions:
x = r * cos(θ)
y = r * sin(θ)
In the given equation, we have r = 2(sin θ - cos θ). Let's substitute these values into the above conversions:
x = 2(sin θ - cos θ) * cos(θ)
y = 2(sin θ - cos θ) * sin(θ)
So, the equation in rectangular coordinates is:
x = 2(sin θ - cos θ) * cos(θ)
y = 2(sin θ - cos θ) * sin(θ)