10.2 Graphs of y = a sin bx and y = a cos bx

  • Period of a Function • Graphs of y = a sin bx and y = a cos bx • Important Values for Sketching

In graphing the function y = sin x ,  we see that the values of y repeat every 2π units of x. This is because sin x  = sin(x  + 2π) = sin(x  + 4π) ,  and so forth. For any function F, we say that it has a period P if F(x) = F(x + P) .  For functions that are periodic, such as the sine and cosine, the period is the x-distance between a point and the next corresponding point for which the value of y repeats.

Let us now plot the curve y = sin 2x .  This means that we choose a value of x, multiply this value by 2, and find the sine of the result. This leads to the following table of values for this function: ...

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