Thread: Graph question

Sketch the graph of y=cos x in the range -pi < or equal to x < or equal to pi
Hence sketch the graph of y=|cos X| in the same range.

From my knowledge of sine and cosine waves i know what the graph will look like, and what the modulus graph will look like, what i dont know is how to prove it. i substituted pi and -pi into cosx and got -1 for both points on the graph, nbut i cant remember how t prove where the turning point is, i know its at (0,1) but i cant prove that without using prior knowledge,

Please help!

Originally Posted by ally79

Sketch the graph of y=cos x in the range -pi < or equal to x < or equal to pi
Hence sketch the graph of y=|cos X| in the same range.

From my knowledge of sine and cosine waves i know what the graph will look like, and what the modulus graph will look like, what i dont know is how to prove it. i substituted pi and -pi into cosx and got -1 for both points on the graph, nbut i cant remember how t prove where the turning point is, i know its at (0,1) but i cant prove that without using prior knowledge,

Please help!

You don't need to prove anything.

The cos curve is the same as the sine curve shift forward by pi/2 radians. And the modulus of that curve is the same, except all the parts that are BELOW the x axis get reflected in the x axis, so that everything is above the axis.