Question

Cartesian euation for r=5 cos theta

Answer 1

The Cartesian equation for r=5cosθ represents a circle with radius 5 and its center at the origin (0,0). The equation relates Cartesian coordinates (x,y) to polar coordinates (r,θ).

Step-by-step explanation:

The Cartesian equation for r = 5 cos θ represents a circle with a radius of 5 units and its center at the origin (0,0). The equation relates the Cartesian coordinates (x, y) to the polar coordinates (r, θ). To convert the polar equation to Cartesian form, we can use the trigonometric identities:

x = r cos θ

y = r sin θ

By substituting the given equation (r = 5 cos θ) into the above formulas, we get:

x = 5 cos θ cos θ = 5 cos² θ

y = 5 cos θ sin θ = 5 sin θ cos θ