Double Angle Equations

Solve the trigonometric equation sin² 2θ = 2sin²θ for θ in the interval [0, π/2)

• 0 and π/4

• 0 and π/6

• 0 and π/2

• π/3 and π/6

Solve the following equation for 0 ≤ x ≤ 2π.  sin 2x cos x = sin x.

• x = 0, π/4, 3π/4, π, 5π/4, 7π/4

• x = 0, -π/4, 3π/4, π, 5π/4, 7π/4

• x = 0, π/4, -3π/4, -π, 5π/4, 7π/4

• x = 0, π/4, -3π/4, π, -5π/4, 7π/4

Solve the following equation for 0 ≤ x ≤ 2π.  cos 2x = cos x

• x = 0, 2π/3, 4π/3

• x = 0, -2π/3, -4π/3

• x = 0, -2π/3, 4π/3

• x = 0, π/, 2π

Solve the following equation for 0 ≤ x ≤ 2π.  sin 2x + sin x = 0

• x = 0, 2π/3, π, 4π/3

• x = 0, -2π/3, π, 4π/3

• x = 0, 2π/3, -π, 4π/3

• x = 0, 2π/3, π, -4π/3

Solve the trigonometric equation sin 2x/(1 + cos 2x) = 1 for θ in the interval [0, π].

• π/4

• π/2

• π/3

• π/6

Solve the following equation for 0 ≤ x ≤ 2π. cos 2x - 1 = sin²x

• x = 0, π

• x = -1, π

• x = 2, π

• x = 0, -π

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant. 

• 120/169

• 25/169

• 60/169

• 5/13

Solve the following equation for 0 ≤ x ≤ 2π.  tan 2x - tan x = 0

• x = 0, π

• x = π/2, π/4

• x = π/6, π/2

• x = π/2, π/3

Solve the following equation for 0 ≤ x ≤ 2π.  cos²x - cos 2x = 0

• x = 0, π

• x = 0, -π

• x = -1, π

• x = 2, π

Solve the equation from [0, 2pi). Given the first two steps, continue to find the solutions for the following equation: Step 1: \(\cos2\theta=\frac{\sqrt{2}}{2}\) Step 2: \(2\theta=\frac{\pi}{4},\frac{7\pi}{4}\)