Question

A wave is modeled with the function y = 1 /2 sin 3 θ , where θ is in radians. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis.

Answer 1

The wave described by y = 1/2 sin 3θ has an amplitude of 1/2, a period of 2π/3 radians, and intersects the x-axis at multiples of π/3. The wave oscillates between +1/2 and -1/2, repeating every 2π/3 radians.

Step-by-step explanation:

The wave function you've provided, y = 1 /2 sin 3 θ, where θ is in radians, is a sine wave with some specific characteristics. To describe the graph of this sine function:

• The amplitude is the coefficient before the sine function, which is 1/2. This means the wave oscillates between +1/2 and -1/2.
• The angular frequency is 3, which affects the period of the function. The period can be found using the formula Period = 2π / frequency, giving us a period of 2π/3 radians.
• Points of intersection with the x-axis (which are also the zeroes of the function) occur when the sine function equals 0. This happens at θ = nπ/3 where n is an integer.

In summary, this function will have a wave-like pattern on its graph, with peaks at 1/2 and troughs at -1/2, and will complete one full cycle every 2π/3 radians.