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

May 12, 2018

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 $\frac{\pi}{3}$ and amplified by 3.

May 12, 2018

As Below.

#### Explanation:

$y = 3 \cos \left(x - \left(\frac{\pi}{3}\right)\right)$

Standard form of cosine function is $y = A \cos \left(B x - C\right) + D$

$\therefore A = 3 , B = 1 , C = \left(\frac{\pi}{3}\right) , D = 0$

$A m p l i t u \mathrm{de} = | A | = 3$

$\text{Period } = P = \frac{2 \pi}{|} B | = 2 \pi$

$\text{Phase Shift ' = -C / B = pi/3, color(crimson)(" pi/3 to the right}$

$\text{Vertical Shift } = D = 0$

Now youcan draw the graph, knowing salient features.

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