The curve above is the graph of a sinusoidal function It goe

The curve above is the graph of a sinusoidal function. It goes through the point (4,3). Find a sinusoidal function that matches the given graph. If needed, you can enter ? as pi in your answer.

I got 3sin(2pi/9*x) but it\'s wrong. Can anyone help me to solve this?

Solution

from graph amplitude is 3 and phase shift is 2 units (the point at which graph crosses the x-axis)
now let the function be of the form y=3sin(k(x-2)) then we need to find variable k using the fact that graph passess through (4,3)
plugging
3=3sin(k*(4-2)) ====> k*(4-2) = pi/2 ====> k = pi/4
so that y= 3sin(pi/4*(x-2))