The letters r and θ represent polar coordinates. Write the following equation using rectangular coordinates (x, y).
Given equation r=5
huh? It's just a circle of radius 5!
r=5
r^2 = 25
x^2+y^2 = 25
Could you explain to me how? I wasn't school when the class was given and I am struggling a bit with it
To convert a polar equation to rectangular coordinates, we can use the following transformations:
x = r * cos(θ)
y = r * sin(θ)
In our case, the given equation is r = 5. To convert this equation into rectangular coordinates (x, y), we can substitute the values of x and y using the above transformation equations:
x = 5 * cos(θ)
y = 5 * sin(θ)
Therefore, the equation in rectangular coordinates (x, y) is:
x = 5 * cos(θ)
y = 5 * sin(θ)
you seem to recall that
x = r cosθ
y = r sinθ
How could you forget that
r^2 = x^2+y^2 ?
Just use the distance formula.
Or, if you insist on trig, recall that
x^2+y^2 = r^2 sin^2θ + r^2 cos^2θ = r^2 (sin^2θ + cos^2θ) = r^2
or, heck - read your math text. It explains it better then I can here, and surely with examples.