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Sin(x) Transformations

Let's explore how a and b in f(x) = a*sin(b*x) can change the sine function! How does sine change as you adjust the values of a and b?
How does a*sin(b*x) change as a incresases? How about as a decreases? How do various values of b affect the period of sine? Can you find values of a and b that half the period of sin(x) and increase the amplitude by a factor of 3?