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.