Need Help Sketching a Sinusoidal Function

Question

Sketch a graph of a sine function whose amplitude is 2, period is 3π, midline is y=1 and y-intercept is (0, 1). The graph is not a reflection of the parent function over the x-axis. Graph at least 1 period of the function.

Could I get some help with this? Having a tough time here.

Answer 1

Normally, the parent function of sin starts at (0,0) Since they tell you the midline is 1 and the y intercept is (0,1) The starting point of your sketch would be (0,1)

The period is 3π. We can divide this by 4 to get 3/4π. This is use to find the x coordinates for your sketch. At 3/4π, the sine hits it max. The y coordinate would go from 1 to 3, since the amplitude is 2)

The next x coordinate would increment again by 3/4π and would hit the midline. The coordinate for this point would be (3/2π,1)

The next point is the mid for the sine function. Again the x coordinate would increment by 3/4π which would bring it to 9/4π. The y value that started at 1, goes down by 2 due to the amplitude. So this point is (9/4π,-1)

Finally,it comes back up to the midline. When we increment by another 3/4π, we hit 3π which is the period, as expected. So the final point is (3π,1)

Points summary for your sketch:

(0,1)

(3/4π,3)

(3/2π,1)

(9/4π,-1)

(3π,1)

This is one period, more can be added to the right or left if needed following the same pattern.