Answer to Question #296564 in Trigonometry for harper

Question

Sketch the graph of the following function in one rectangular coordinate plane. Compare the behavior of each of the following graphs to the graph of y = sin x in terms of period, amplitude, and phase shift.

y=2sin x-4

y=sin 2x+3π2

y=sin 2x+2

Answer 1

Explanations & answer

• Here is the picture of the graphs attached. You can refer to it.

• Y = Sin(x) is shown in the middle in dotted line.
• Whenever there is a variation to that function it behaves like follows.
• Y = 2Sin(x), function gets stretched along the Y-axis by a factor of 2 and Y = 2Sin(x) - 4 gets its middle axis shifted to the negative Y side (down) in 4 units. Hence the amplitude is increased by a factor of 2, with no phase shift and no change in period.

• Y = sin(2x) gets its period reduced by a factor of 2. Then Y = Sin(2x+3$\small \pi$/2) gets a negative phase shift (shifts to left of x-axis). This would be the other way around if there was -3$\small \pi$/2 instead. Finally, there is no change in amplitude as the coefficient is 1 same as Y =Sin(x).

• The last one is a combination of the previous two scenarios. It has its period reduced by 2 and the middle axis shifted in positive 2 along Y-axis (upwards). There is amplitude change as well as phase shift.