precalculus: Graph the cosine function

Question

Graph the function. Show at least one period.

 y=2cos(−5𝑥+𝜋)

Answer 1

Hi Katelyn A.,

y = 2cos(-5x+π), is the same as y = 2cos[(-)(5x - π)]. And since cos(-x) = cos(x), we can take out the negative leaving y = 2cos(5x - π).

For this trig. function, the amplitude is 2, the period is 2π/5, and the horizontal (phase) shift is π/5 to the right.

To Graph (two periods):

X-axis spacing of π/10.

Plot points (π/5, 2); (3π/10, 0); (2π/5, -2); (π/2, 0); (3π/5, 2); (7π/10, 0); (4π/5, -2); (9π/10, 0); (π, 2).

Connect points for graph.

I hope this helps, Joe.