Trigonometric Functions and the Unit Circle

The video tutorial introduces the unit circle and its application in defining trigonometric functions for angles beyond 90 degrees, including negative angles. It demonstrates how to calculate sine and cosine values for various angles, both in degrees and radians, using the unit circle. The tutorial emphasizes understanding the unit circle's role in trigonometry and provides examples for practice.

What is the primary purpose of the unit circle in trigonometry?

• To define trigonometric functions for angles greater than 90 degrees and negative angles.

• To simplify the calculation of trigonometric functions.

• To replace the traditional SOHCAHTOA definition.

• To provide a visual representation of angles.

What is the relationship between the unit circle and the traditional SOHCAHTOA definition?

• The unit circle contradicts SOHCAHTOA.

• The unit circle is an extension of SOHCAHTOA.

• The unit circle simplifies SOHCAHTOA.

• The unit circle is a replacement for SOHCAHTOA.

What is the sine of 275 degrees on the unit circle?

• -0.819

• 0.819

• -0.996

• 0.996

How is the sine of a negative angle, such as -55 degrees, determined on the unit circle?

• By finding the x-coordinate of the point.

• By finding the y-coordinate of the point.

• By calculating the angle clockwise from the positive x-axis.

• By using the cosine function.

What is the sine of 285 degrees?

• 0.819

• -0.819

• -0.966

• 0.966

What is the approximate decimal value of the sine of 2/3 pi radians?

• 0.819

• 0.866

• 0.259

• 0.996

What is the significance of the value 0.866 in the context of the unit circle?

• It is the cosine of 2 pi radians.

• It is the sine of 15 degrees.

• It is the cosine of 112 pi radians.

• It is the sine of 2/3 pi radians.

What is the sine of 15 degrees?

• 0.996

• 0.259

• 0.819

• 0.866

What is the cosine of 2 pi radians?

• 0

• 1

• -1

• 0.5

What is the x-coordinate of the point for the cosine of 112 pi radians?

• 0.966

• 1

• 0

• -0.966