How do I convert
theta = 45 degrees
Into a rectangular equation?
x = y
Ok Here's how you get there:
x = r cos theta = r (sqrt2)/2
y = r sin theta = r (sqrt2)/2
y/x = tantheta = tan45 = 1
x = y
To convert the given polar equation θ = 45 degrees into a rectangular equation, you need to understand the relationship between polar and rectangular coordinates.
In the rectangular coordinate system, a point is represented by its x and y coordinates. On the other hand, in the polar coordinate system, a point is represented by its distance from the origin (r) and the angle it forms with the positive x-axis (θ).
To convert a polar equation into a rectangular equation, you can use the following equations:
x = r * cos(θ)
y = r * sin(θ)
Considering θ = 45 degrees, let's substitute it into these equations:
x = r * cos(45)
y = r * sin(45)
We know that cos(45) = sin(45) = 1/√2 ≈ 0.7071. Therefore:
x = r * 0.7071
y = r * 0.7071
This gives us a pair of equations that relate x and y to r. These equations, x = r * 0.7071 and y = r * 0.7071, represent the rectangular equation of the given polar equation θ = 45 degrees.