Cosine Function Properties and Transformations

The video tutorial explains how to analyze a cosine function by determining its amplitude, period, and phase shift. It reviews the properties of sine and cosine functions, including amplitude, reflection, period, and translations. An example is provided to illustrate these concepts, followed by a graphical verification to confirm the analysis. The tutorial aims to help viewers understand and apply these concepts to cosine functions.

What is the amplitude of a cosine function when the absolute value of 'a' is 5?

• 2.5

• 5

• 10

• 0

Tags

CCSS.HSF-IF.C.7E

If 'a' is negative in a cosine function, what effect does it have on the graph?

• No effect

• Vertical stretch

• Reflection across the midline

• Horizontal shift

Tags

CCSS.HSF-IF.C.7E

How is the period of a cosine function calculated?

• 2π/b

• a/2π

• 2π/a

• b/2π

Tags

CCSS.HSF-IF.C.7E

What happens to the graph of a cosine function if 'c' is positive?

• Shifted down

• Shifted up

• Shifted left

• Shifted right

In the context of horizontal translation, what does a positive 'd' indicate?

• Vertical shift

• No shift

• Shift right

• Shift left

Tags

CCSS.HSF-IF.C.7E

In the given example, what is the value of 'a' and what does it imply?

• 0, no reflection

• 3, no reflection

• 7, no reflection

• -7, reflection across midline

Tags

CCSS.HSF.TF.A.4

What is the period of the example cosine function?

• 2π

• π

• 2π/3

• π/2

Tags

CCSS.HSF-IF.C.7E

What is the phase shift of the example cosine function?

• No shift

• π/5 to the right

• π/5 to the left

• π/3 to the right

Tags

CCSS.HSF-IF.C.7E

What is the maximum value of the cosine function in the example?

• 0

• 7

• -7

• 3

Tags

CCSS.HSF-IF.C.7E

What pattern does the reflected cosine function follow over one period?

• Maximum, midline, minimum, midline, maximum

• Minimum, midline, maximum, midline, minimum

• Midline, maximum, midline, minimum

• Maximum, minimum, maximum

Tags

CCSS.HSF-IF.C.7E