Trigonometric Equations Worksheets Grade 11

1. Solve: 3tan²(x) - 5tan(x) - 2 = 0 for x ∈ [0, 2π].
2. Aroha is a telecommunications engineer modeling signal interference between two radio towers. The combined signal strength at a receiver is given by the equation 9 cos²θ - 12 cosθ + 4 = 0, where θ is the phase difference in radians between the two signals. Find all solutions for θ in the interval [0, 2π).
3. Mere is an audio engineer designing an active noise cancellation system for an industrial workspace. Two speakers generate sound waves that interfere destructively. The net sound pressure level at a specific sensor is given by the equation 12 cos²θ - 5 cosθ - 2 = 0, where θ is the phase difference between the two waves in radians, measured in the interval [0, 2π). Determine all possible phase differences θ that produce perfect silence (zero net pressure) at the sensor.

…and 5 more problems

1. Charlotte is a sound engineer designing an audio cancellation system for a concert hall. Two speakers emit sound waves that interfere with each other. The combined sound pressure level at a certain seat is modeled by the equation 5sin²θ - 8sinθ + 3 = 0, where θ represents the phase shift between the two sound waves in radians, measured from 0 to 2π. Find all possible phase shifts θ in the interval [0, 2π) that result in zero sound pressure at that seat.
2. 2cos²(x) - √3cos(x) = 0 for x ∈ [0, 2π]
3. 2sin²(x) - 1 = 0 for x ∈ [0, 2π]

…and 4 more problems

1. A right triangle is drawn on a coordinate plane with vertices at (0,0), (4,0), and (4,3). The angle θ is located at the origin, between the positive x-axis and the hypotenuse. Find the exact value of sin(2θ) using trigonometric identities.
2. Sophia is an acoustic engineer designing noise-canceling headphones. The interference pattern between the ambient noise and the anti-noise wave can be modeled by the equation 8cos²θ - 14cosθ + 5 = 0, where θ represents the phase angle between the two waves in radians, measured from 0 to 2π. Find all possible phase angles θ in the interval [0, 2π) that result in perfect destructive interference (zero net sound).
3. 2sin²(x) - sin(x) - 1 = 0 for 0 ≤ x ≤ 2π

…and 4 more problems