Understanding Amplitude and Period of Sine and Cosine Functions

This video tutorial covers the amplitude and period of sine and cosine functions. It explains periodic functions, how to determine the period and amplitude, and how these concepts affect the graphing of functions. The video also demonstrates graphing techniques for functions with different amplitudes and periods, providing a comprehensive understanding of these mathematical concepts.

What is the primary goal of this video lesson?

• To understand the amplitude and period of sine and cosine functions

• To learn about horizontal and vertical translations

• To explore the history of trigonometric functions

• To solve complex trigonometric equations

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CCSS.HSF.TF.A.4

What is the period of a basic sine function?

• PI

• 2PI

• 3PI

• 4PI

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CCSS.HSF-IF.C.7E

How does the value of B affect the period of the function Y = sin(BX)?

• It doubles the period

• It has no effect on the period

• It changes the period to 2PI/B

• It halves the period

Tags

CCSS.HSF.TF.A.4

What is the period of the function Y = cos(3X) in radians?

• 2PI

• 3PI

• PI

• 2PI/3

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CCSS.HSF-IF.C.7E

How do you determine the period of Y = sin(X/4)?

• 2PI

• 8PI

• PI/2

• 4PI

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CCSS.HSF-IF.C.7E

What is the amplitude of the function Y = 3 sin(X)?

• 4

• 3

• 2

• 1

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CCSS.HSF-IF.C.7E

How is the amplitude of a function defined?

• The distance between two peaks

• The width of the wave

• The distance from the center to the maximum or minimum

• The total height of the wave

Tags

CCSS.HSF-IF.C.7E

What happens to the graph of Y = -2 sin(X) compared to Y = sin(X)?

• It compresses horizontally

• It reflects across the X-axis

• It shifts upwards

• It stretches vertically

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CCSS.HSF-IF.C.7E

What is the amplitude of Y = 1/2 cos(2X)?

• 1/2

• 3

• 2

• 1

Tags

CCSS.HSF-IF.C.7E

In the function Y = -2 sin(3X), what is the effect of the negative sign?

• It increases the amplitude

• It decreases the period

• It reflects the graph across the X-axis

• It shifts the graph to the right

Tags

CCSS.HSF-IF.C.7E