Sketch two complete cycles of the graph, then answer the question about the function. How is the graph related to its parent graph y=sinx or y=cosx

Question

1) y=5 sin2x

2)y=3 cos(x/2)

3)y=2 sin(2Πx)+1

 

Answer 1

Aria,

 

You have 3 things going on here.

1) The coefficients 5, 3 and 2 stretch the original graph the respective amount. Whereas the original graph goes from -1 to 1 [-1,1], the graph for 5sin2x for example goes from -5 to 5. [-3,3] and [-2,2] for the other two.

2) The 2, 1/2 and 2∏ change the frequency of the sinusoid. In other word they stretch or compress the original graph. If they are greater than 1 (2, and 2∏ are), they compress the graph by that much. If they are less than 1 (/12 is) then the original graph is stretched along the x-axis.   

3) Adding a constant to any function only moves the original graph up or dawn depending on the sign of the constant. 1 of 2sin(2∏x) + 1 just moves the graph up 1 unit.