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These functions are very pleasant to draw because we know anything about them:)
1. y(x) = cos(x), 0<=x<=180°.
cos(x) has one root at x=90°, is >0 for 0<=x<90° and is<0 for 90°<x<=180°.
Also, y(0)=1 (the only maximum) and y(180°)=-1 (the only minimum).
And y(x) is monotone decreasing. Also it is convex up for 0<=x<90 and convex down for 90<x<=180, so having a bend at x=90°.
Please look at the pictures cosx.png (created by hand) and cosxw (by a graphing utility, x marked in radians).
2. y(x) = sin2x, 0°<=x<=180°.
y has three roots, at x=0, x=90° and x=180°. y>0 for 0°<x<90° and <0 for 90<x<180. It has one maximum at x=45° (y=1) and one minimum at x=135° (y=-1).
y is increasing from 0 to 45°, decreasing from 45° to 135° and again increasing from 135° to 180°.
It is convex up from 0 to 90 and convex down from 90 to 180°.
Please look at the picture sin2xw.png (by graphing utility).
Please ask me if anything is unclear or missing.
This is simple ....it is as follows
Y=cosx For 0<=x<=180
Now by applying cos ,we get
so the cos(x) function lies in between -1,1
y= sin 2x for 0<=x<=180
multiplying with 2 , we get
now applying sin function , we get
now let see the graphs in the attachments given below
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