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

2 Answers
May 12, 2018

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


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.
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May 12, 2018

As Below.


#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]}