Identify the curve by finding a cartesian equation for the curve

r cos(theta)=1

PLEASE EXPLAIN! thanks!

The conversion from polar coordinates to cartesian coordinates uses the transformation:
r = √(x² + y²)
Θ = arctan(y/x)
cosΘ = x/r = x/√(x²+y²)

Making the substitutions:
[√(x²+y²)][x/√(x²+y²)] = 1
x = 1

The curve is the straight line parallel to the y-axis, x = 1

Recall that the transformation between rectangular and polar coordinates is x = r cos(theta) and y = r sin(theta). So what you have is
1 = r cos(theta) = x
So x = 1 is a vertical line in the Cartesian coordinate system