Math CentralQuandaries & Queries


Question from Kapilan, a student:

When graphing trigonometric functions like SIN and COSINE does f(x)=x
squared equal to SIN or COSINE

Also what is the range, domain, period and amplitude for y=sin@ + 3

Thank you very much

Hi Kapilan,

No matter what value of x you use, sin(x) and cos(x) are always between -1 and +1. f(x) = x2 has the value 32 = 9 when x = 3 so x2 can't be sin(x) or cos(x).

Let's look at y = sin(x) + 3 which is, I think, the function you are asking about. To evaluate this function at some x value, say x = 30 degrees, you first evaluate sin(30o) and then add 3 to the result. So all the term +3 does is add 3 to the value of sin(x). Hence to see the graph of f(x) = sin(x) + 3 take the graph of sin(x) and lift it up 3 units. Thus the domain, period and amplitude of f(x) = sin(x) + 3 are the same as the domain, period and amplitude of sin(x). Only the range has changed.

I hope this helps,

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