Graphing the Cosine Graph with Multiple Transformations

The video tutorial explains how to graph a trigonometric function without using a calculator. It covers essential elements like amplitude, period, X scale, and phase shift. The instructor demonstrates how to calculate these elements and apply transformations, including reflection and phase shift, to graph the function accurately. Tips for beginners are provided to ensure understanding and correct application of graphing techniques.

What is the first step in graphing a trigonometric function?

• Identify the amplitude

• Determine the phase shift

• Find the vertical translation

• Calculate the X scale

How do you calculate the period of a trigonometric function?

• Divide 2π by the coefficient of X

• Multiply the amplitude by 2

• Add the phase shift to the X scale

• Subtract the vertical translation from the amplitude

What is the X scale if the period is π/2?

• π

• π/16

• π/8

• π/4

How is the phase shift determined in a trigonometric function?

• By adding the amplitude to the period

• By setting the inside of the function equal to zero

• By finding the maximum value of the function

• By calculating the difference between the highest and lowest points

What effect does a negative amplitude have on the graph of a trigonometric function?

• It decreases the X scale

• It shifts the graph to the right

• It reflects the graph over the X-axis

• It increases the period

When graphing a cosine function, where do you start if there is a reflection over the X-axis?

• At the phase shift

• At the origin

• At the minimum point

• At the maximum point

What is the final step in graphing a transformed trigonometric function?

• Calculate the new period

• Find the new X scale

• Apply the vertical translation

• Determine the new amplitude