Find all values of [theta] in the interval 0°<=X<= 360° that satisfy the equation cos2[theta]-cos[theta]=0
costheta(costheat-1)=0
costheta=0
or costheta=1
what satisfies that
To find all the values of θ in the given interval that satisfy the equation cos²θ - cosθ = 0, we can solve the equation step by step:
1. Factor out a common term: cosθ(cosθ - 1) = 0
2. Apply the zero product property: Either cosθ = 0 or cosθ - 1 = 0
3. Solve for cosθ = 0: In the unit circle, the cosine function is 0 at θ = 90° and θ = 270°.
4. Solve for cosθ - 1 = 0: Add 1 to both sides to get cosθ = 1. In the unit circle, the cosine function is 1 at θ = 0° and θ = 360°.
5. Therefore, the solutions for θ are: 0°, 90°, 270°, and 360°.