Question

Solve on the interval [0,2pi): 1-costheta=2-square3/2

Answer 1

• Answer:

The solutions of the original equation on the interval: [0, 2π) is:

Option (A): π/6, 5π/6

• Explanation:

The solutions of the original equation on the interval are:

[0, 2π) is: Option (A): π/6, 5π/6

• Multiply both sides by 2:

2(1 - cos θ) = 2( 2 - √3 / 2)

• Simplify:

2 - 2 cos θ = 2 - √3

• Add: 2 cos θ to both sides:

2 = 2 cos θ + √3

• Subtract 2 from both sides:

0 = 2 cos θ + √3 - 2

• Add 2 to both sides:

2 = 2 cos θ + √3

• Subtract √3 from both sides:

2 - √3 = 2 cos θ

• Divide both sides by 2:

2 - √3/2 = cos θ

• Find the angles:

θ = arcos(2 - √3/2)

• Calculate the angles:

θ = π/6, 5π/6

• Draw a conclusion:

The solutions of the original equation on the interval are:

[0, 2π) is: Option (A): π/6, 5π/6

Hope it helps!