Graphing Sine and Cosine Functions: Transformations and Techniques

This video tutorial covers how to graph sine and cosine functions, including their transformations. It begins with an introduction to the basic sine and cosine graphs using the unit circle. The tutorial then explains how to apply transformations such as amplitude changes, period adjustments, reflections, and shifts to these graphs. Through various examples, viewers learn to graph complex sine and cosine functions with multiple transformations, enhancing their understanding of trigonometric graphing.

What is the amplitude of a sine function with a vertical stretch of 2?

• Amplitude is 2

• Amplitude is 4

• Amplitude is 1

• Amplitude is 0.5

How does the period of a sine function change when multiplied by 1/2?

• Period is quadrupled

• Period remains the same

• Period is doubled

• Period is halved

What effect does a negative sign have on a cosine graph?

• Shifts the graph upwards

• No effect

• Reflects the graph across the x-axis

• Shifts the graph downwards

What is the new period when the cosine function is multiplied by 2?

• 1/2 Pi

• 4 Pi

• 2 Pi

• Pi

How does a phase shift of Pi/4 to the right affect the graph?

• Shifts the graph Pi/2 units to the right

• Shifts the graph Pi/4 units to the right

• Shifts the graph Pi/4 units to the left

• No shift occurs

What is the vertical shift of the function y = 3 sin(x) - 3?

• No vertical shift

• Shifts up by 3 units

• Shifts up by 1 unit

• Shifts down by 3 units

What is the amplitude of the function y = 3 sin(x)?

• 3

• 1

• 0

• 6

What does a factor of Pi/4 in the cosine function indicate about the period?

• Period is 2 Pi

• Period is 8

• Period is 4

• Period is Pi/4

How does a horizontal shift of +2 affect the cosine graph?

• No shift

• Shifts right by 2 units

• Shifts left by 2 units

• Shifts left by 4 units

What is the effect of a vertical shrink by 1/2 on the sine graph?

• No change in amplitude

• Halves the amplitude

• Doubles the amplitude

• Quadruples the amplitude