Question

Solve the system r=cosθ,r=1−cosθ.

A) Polar Coordinates
B) Parametric Equations
C) Exponential Decay
D) Logarithmic Functions

Answer 1

To solve the system r=cosθ, r=1−cosθ using polar coordinates, substitute the second equation into the first equation, add cosθ to both sides, divide both sides by 2, and take the inverse cosine of both sides.

Step-by-step explanation:

To solve the system r=cosθ, r=1−cosθ using polar coordinates:

1. Substitute the second equation into the first equation: cosθ = 1−cosθ.
2. Add cosθ to both sides of the equation: 2cosθ = 1.
3. Divide both sides by 2: cosθ = 1/2.
4. Take the inverse cosine of both sides: θ = cos-1(1/2).

Therefore, the solution to the system in polar coordinates is θ = cos-1(1/2).