convert from rectangular coordinates to polar coordinates x=y
x/r = cosØ ---> x = rcosØ
y/r = sinØ ---> y = rsinØ
rcosØ = rsinØ
sinØ/cosØ = 1
tanØ = 1
Ø = π/2
which makes sense to me,
x = y is a straight line with (0,0) as the intercept and a 45° angle
Ø = 45° is the correct angle of our line, since no restriction is placed on r, r can be any length, so it is the same straight line
thank you
To convert from rectangular coordinates to polar coordinates, we need to use the following equations:
r = √(x^2 + y^2)
θ = arctan(y / x)
Given that x = y, we can substitute y for x in these equations. Let's solve for r first:
r = √(x^2 + y^2)
= √(x^2 + x^2)
= √(2x^2)
= x√2
Next, let's solve for θ:
θ = arctan(y / x)
= arctan(y / y)
= arctan(1)
= π/4 radians
Therefore, the polar coordinates for x = y are (r, θ) = (x√2, π/4).