Algebra 2 Question - Tangent Functions

Question

A wave is modeled with the function y=1/2sin(3θ), 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

A general sine function has the form:

y = a·sin(b(θ-c)) + d

1. a = amplitude
2. b = angular frequency (radians/sec) = 2π/period.
3. c = phase (horizontal) shift
4. d = vertical shift

You function is:

y = (1/2)·sin(3(θ-0)) + 0 = (1/2)·sin(3θ)

1. a = amplitude = 1/2
2. b = angular frequency = 3 = 2π/period, so period = 2π/3
3. c = phase shift = 0 (no phase shift)
4. d = vertical shift = 0 (no vertical shift)

It intersects the x-axis when y = 0

0 = (1/2)·sin(3θ)

which occurs when 3θ = ± n·π, n = 0, 1, 2, 3, 4, ..., or θ = ± n·π/3, n = 0, 1, 2, 3, 4,