# How do you graph y=cos(2x) over the interval 0<=x<=360?

Jul 15, 2017

Remember the $\cos$ function has the following points:
$\left(0 , 1\right) , \left(90 , 0\right) , \left(180 , - 1\right) , \left(270 , 0\right) , \left(360 , 1\right)$

#### Explanation:

But because it $2 x$ the period is shortened. It will reach its $0 -$point after only 45, the $- 1$ after 90, etc.

So the points are now:
$\left(0 , 1\right) , \left(45 , 0\right) , \left(90 , - 1\right) , \left(135 , 0\right) , \left(180 , 1\right) , \left(225 , 0\right) , \left(270 , - 1\right) , \left(315 , 0\right) , \left(360 , 1\right)$
(vertical axis on the graph below should be read as 100=1)
graph{100cos(2pix/180) [-27.8, 453, -127.5, 113.2]}

Jul 15, 2017

Graph would look like as shown below.

#### Explanation:

Select a trignometric graph and plot the following points and join with a smooth curve, as shown. This completes two cycles of this periodic function.

(0,1) ; (pi/4,0); (pi/2, -1); ((3pi)/4,0) :( pi, 1); ((5pi)/4,0); ((3pi)/2, -1); ((7pi)/4, 0) and (2pi, 1).

Join the points with a smooth curve as shown in the graph.

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