Understanding Sine and Cosine Functions

This video tutorial covers the graphing of sine and cosine functions using the unit circle. It explains how to determine the domain, range, and period of these functions. The video includes demonstrations using Wolfram to visualize the sine and cosine graphs, highlighting key points and values. It also discusses the concept of periodic functions, emphasizing the properties of sine and cosine, such as their symmetry and periodicity. The tutorial concludes with a summary of the key concepts covered.

What is the primary goal of the video regarding sine and cosine functions?

• To learn about tangent functions

• To understand complex numbers

• To graph sine and cosine functions using the unit circle

• To solve trigonometric equations

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In the unit circle, what does the y-coordinate represent?

• Tangent of the angle

• Sine of the angle

• Cosine of the angle

• Cotangent of the angle

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What is the period of the sine function as demonstrated in the video?

• 3PI radians

• 2PI radians

• 4PI radians

• PI radians

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When plotting the sine function manually, what is the amplitude?

• 0.5

• 1

• 2

• 3

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What is the x-coordinate equal to on the unit circle?

• Sine of the angle

• Cosine of the angle

• Secant of the angle

• Tangent of the angle

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What is the period of the cosine function?

• 3PI radians

• 2PI radians

• PI radians

• 4PI radians

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What is a characteristic of a periodic function?

• It is always decreasing

• It is always increasing

• It repeats at regular intervals

• It has a constant slope

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What is the symmetry property of the cosine function?

• Symmetrical about the origin

• Symmetrical across the y-axis

• Symmetrical across the x-axis

• No symmetry

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What is the range of both sine and cosine functions?

• From -2 to 2

• From -1 to 1

• From 0 to 1

• From -1 to 0

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What is the relationship between sine of negative theta and sine of theta?

• Sine of negative theta is equal to negative cosine of theta

• Sine of negative theta is equal to cosine of theta

• Sine of negative theta is equal to negative sine of theta

• Sine of negative theta is equal to sine of theta

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