Find the Horizontal Shift

Question

y=-2cos(1/4x- pi/2)

Find the horizontal shift of this problem.

Answer 1

Using Mark H.'s nomenclature, function could be rewritten y = -2 cos (ω(t + θ)). Then the phase shift is -θ..

In this case y = -2 cos (1/4(t + 2π))

The phase shift if 2π to the left,

An alternative is using the given equation. Then the phase shift is -θ/ω that is (-π/2) / (1/4) that results in -2π the same shift to the left.

Answer 2

One general equation for a sinusoidal function is y = Asin(ωt + θ), where:

A is the 1/2 amplitude (0 to peak), ω is the frequency in radians/sec, and θ is the phase shift. (The reference point is where the sin is zero)

Note that cos(x) is the same as sin(x + pi/2). Thus, we need to know what the reference point is for "shift" in your problem.