Graphing Cosine Functions Concepts

The video tutorial explains how to sketch the graph of the function f(theta) = 3cos(theta - pi/2) + 1. It covers identifying the values of a, b, d, and c, which determine the transformations of the cosine function. The tutorial discusses amplitude, period, phase shift, and vertical shift, and how these affect the graph. It provides a step-by-step guide to graphing the function, including dividing the period into sub-intervals and following the cosine pattern. The video concludes with tips on using graphing tools to complete the graph.

What is the function we are asked to graph?

• f(θ) = 3 cos(θ - π/2) + 1

• f(θ) = 3 tan(θ - π/2) + 1

• f(θ) = 3 sec(θ - π/2) + 1

• f(θ) = 3 sin(θ - π/2) + 1

What is the amplitude of the function?

• 1

• 2

• 3

• 4

What is the period of the function?

• 2π

• 4π

• π

• π/2

What is the phase shift of the function?

• Right π

• Left π/2

• Right π/2

• Left π

What is the vertical shift of the function?

• Up 1 unit

• Down 1 unit

• Up 2 units

• Down 2 units

Where is the midline of the function located?

• y = -1

• y = 2

• y = 1

• y = 0

What is the pattern followed when graphing the basic cosine function over one period?

• Maximum, Midline, Minimum, Midline, Maximum

• Midline, Maximum, Midline, Minimum, Midline

• Minimum, Midline, Maximum, Midline, Minimum

• Minimum, Maximum, Midline, Minimum, Maximum

At which x-value does the graph of the function start due to the phase shift?

• x = 2π

• x = π/2

• x = π

• x = 0

What is the maximum value of the cosine function after considering the amplitude and vertical shift?

• 5

• 4

• 3

• 2

Which tool is suggested for graphing the function in homework?

• A tool for secant functions

• A tool for cosine functions

• A tool for tangent functions

• A tool for sine functions