Question

How do you graph `y= 3cos(x-pi/3)`?

Answer 1

Calculate the desired number of data points, and put them on an appropriate graph paper.

Explanation:

ANY graphing or plotting must start with a table of values of the independent variable and the evaluated expression. With those values you may plot them on graph paper manually, or use a computer plotting program.

Sometimes, we just want a rough sketch, in which case recognizing the general forms of common equations such as lines, parabolas, and cubics is helpful. In this case we have a cyclic function (cos) that is off-set by `pi/3` and amplified by 3.

Answer 2

As Below.

Explanation:

`y = 3 cos(x - (pi/3))`

Standard form of cosine function is `y = A cos (Bx - C) + D`

`:. A = 3, B = 1, C = (pi/3), D = 0`

`Amplitude = |A| = 3`

`"Period " = P = (2pi) / |B| = 2pi`

`"Phase Shift ' = -C / B = pi/3, color(crimson)(" pi/3 to the right"`

`"Vertical Shift " = D =0`

Now youcan draw the graph, knowing salient features.

graph{3 cos(x - (pi/3)) [-10, 10, -5, 5]}