Q. Respected Sir/Madam; Sketch the graph of `y=sin^2x + 2cos^2x`

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Sketch the graph of `y=sin^2x+2cos^2x` :

We can rewrite the right hand side:

`y=sin^2x+cos^2x+cos^2x` Use the Pythagorean relation:

`y=1+cos^2x`

So we take the values of cosx, square them, and add them to one. The values will oscillate between 1 and 2 (`0<= cosx<=1 ==> 0<=cos^2x<=1` , then you add 1.) The period is `pi` .

The graph:

 

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