4e Example 4 (Write the trig function given the transformations)

The video tutorial covers writing equations for trigonometric functions, focusing on sine, cosine, and tangent. It explains how to determine the amplitude, period, phase shift, and vertical shift for each function. The sine function is analyzed with an amplitude of 4, a period of 4π, and a vertical shift up by 1. The cosine function is explored with a phase shift of π to the right and a reflection about the x-axis. The tangent function is discussed with a period of π/2, a reflection about the y-axis, and a vertical shift down by 2. The tutorial emphasizes understanding transformations and checking work for accuracy.

What is the amplitude of the sine function if it is given as 4?

• 1

• 2

• 4

• 8

How do you calculate the period of a sine function?

• π / B

• 2π / B

• 2π / A

• π / A

What is the effect of a phase shift of π to the right on a cosine function?

• Shift the graph π units to the left

• Shift the graph π units to the right

• Reflect the graph over the x-axis

• Reflect the graph over the y-axis

What happens to the cosine function when it is reflected about the x-axis?

• The graph shifts horizontally

• The graph shifts vertically

• The period changes

• The amplitude becomes negative

What is the original period of the tangent function?

• π

• 4π

• 2π

• π/2

How does a reflection about the y-axis affect the tangent function?

• It changes the amplitude

• It changes the sign of B

• It changes the vertical shift

• It changes the period

What is the vertical shift if the tangent function is shifted down by 2 units?

• +2

• -2

• +1

• -1