The graph of a sine function is drawn. One full cycle goes from x=0 to x=2pi/5 and the low point on that cycle is (pi/10-3). Which of the following functions could have this graph?
a) y=3 sin (1/5x)
b) y=3 sin 5x
c) y=5 sin 3x
d) y=-3 sin 5x
The general equation for a sine function is y = a sin(bx), where 'a' is the amplitude and 'b' is the frequency.
From the given information, we can determine that the amplitude is 3 because the low point on the graph is at y = (pi/10 - 3). This means that the maximum value is 3 and the minimum value is -3.
The full cycle of the function goes from x = 0 to x = 2pi/5. The period of a sine function is given by 2pi/b, where 'b' is the frequency. In this case, 2pi/b = 2pi/5, so b = 5.
Therefore, the correct function that could have this graph is:
b) y = 3 sin 5x