Transformations of Sine and Cosine Functions

This video tutorial covers the transformations of sine and cosine functions, focusing on horizontal and vertical translations. It explains how to determine these translations and graph the functions accordingly. The video includes examples of translating sine and cosine functions, demonstrating the process step-by-step. It concludes with a graphing calculator demonstration to visualize the transformations.

What is the main focus of the second video in the series?

• Amplitude and period of sine and cosine functions

• Solving trigonometric equations

• Horizontal and vertical translations of sine and cosine functions

• Graphing basic sine and cosine functions

If D > 0 in the equation y = sin(x - D), which direction does the graph shift?

• Right D units

• Up D units

• Down D units

• Left D units

In the equation y = cos(x + D), what happens when D < 0?

• The graph shifts left D units

• The graph shifts right D units

• The graph shifts up D units

• The graph shifts down D units

What is the effect of a positive C in the equation y = sin(x) + C?

• The graph shifts left C units

• The graph shifts right C units

• The graph shifts down C units

• The graph shifts up C units

How does the graph of y = cos(x) - 1/2 change?

• It shifts left 1/2 unit

• It shifts down 1/2 unit

• It shifts right 1/2 unit

• It shifts up 1/2 unit

In the example y = sin(x - π/4) + 1, what is the horizontal shift?

• Left π/4 units

• Right π/4 units

• Up π/4 units

• Down π/4 units

For the function y = sin(x - π/4) + 1, what is the vertical shift?

• Up 1 unit

• Right 1 unit

• Down 1 unit

• Left 1 unit

In the function y = -1/2 + cos(x + π/2), what is the horizontal shift?

• Down π/2 units

• Left π/2 units

• Right π/2 units

• Up π/2 units

What is the vertical shift in the function y = -1/2 + cos(x + π/2)?

• Left 1/2 unit

• Down 1/2 unit

• Up 1/2 unit

• Right 1/2 unit

What is the new center line for the function y = -1/2 + cos(x + π/2)?

• y = 0

• y = -1

• y = -1/2

• y = 1/2