Unit Circle and Trigonometric Functions

This video tutorial explains how to graph the sine and cosine functions by mapping values from the unit circle onto the Cartesian plane. It introduces the concept of the wrapping function and defines new functions x(t) and y(t) to represent cosine and sine, respectively. The tutorial demonstrates how to plot these functions on a graph, using specific angles and coordinates from the unit circle. It also discusses the differences between the x and y values on the unit circle and those on the graph, providing a comprehensive understanding of how to visualize these trigonometric functions.

What is the primary purpose of using the unit circle in graphing sine and cosine functions?

• To find the circumference of the circle

• To calculate the area of the circle

• To map real numbers to points on the circle

• To measure angles in degrees

What do the functions x(t) and y(t) represent in terms of the unit circle?

• x(t) is the y-coordinate and y(t) is the x-coordinate

• x(t) is the radius and y(t) is the angle

• x(t) is the angle and y(t) is the radius

• x(t) is the x-coordinate and y(t) is the y-coordinate

How is the sine function plotted on the Cartesian plane?

• Using the angle in degrees

• Using the radius of the unit circle

• Using the y-coordinate from the unit circle

• Using the x-coordinate from the unit circle

What is the y-coordinate of the sine function when theta is pi?

• 0.5

• -1

• 0

• 1

What is the x-coordinate of the cosine function when theta is 0?

• -1

• 1

• 0

• 0.5

How does the shape of the cosine function compare to the sine function?

• It is a different shape

• It is a vertical reflection

• It is the same shape but shifted

• It is a mirror image

What is the typical label for the independent variable in function graphs?

• Theta

• X

• T

• Y

In the context of the unit circle, what does the x-coordinate represent in the graph of the cosine function?

• The radius of the unit circle

• The y-coordinate of the unit circle

• The angle in radians

• The x-coordinate of the unit circle

What is a common source of confusion for students when graphing these functions?

• The difference between radians and degrees

• The use of x and y on the unit circle versus the graph

• The calculation of the unit circle's circumference

• The conversion between sine and cosine

What is the range of the sine and cosine functions?

• Between -1 and 1

• Between -2 and 2

• All real numbers

• Between 0 and 1