Trigonometric Functions and Unit Circle

The video tutorial introduces trigonometric functions and their limitations when defined using right triangles. It then extends these definitions using the unit circle, allowing for angles beyond 90 degrees and less than 0. The tutorial explains how sine, cosine, and tangent can be defined using the unit circle, providing examples to illustrate these concepts. The video concludes with a promise to graph these functions in the next module.

What does the mnemonic 'sohcahtoa' help you remember?

• The properties of circles

• The Pythagorean theorem

• The definitions of sine, cosine, and tangent

• The order of operations

Why does the right triangle definition of trigonometric functions break down at certain angles?

• Because it only works for angles greater than 90 degrees

• Because it requires a circle

• Because it requires a square

• Because it only works for angles less than 90 degrees

What is the radius of the unit circle?

• 1

• 3

• 2

• 0

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

• Cosine of the angle

• Secant of the angle

• Tangent of the angle

• Sine of the angle

How is the tangent of an angle defined using the unit circle?

• x^2 + y^2

• x - y

• x/y

• y/x

What is the sine of pi/2 radians?

• -1

• 1

• 0

• Undefined

What is the cosine of pi radians?

• -1

• 1

• 0

• Undefined

What happens to the tangent function at pi/2 radians?

• It is undefined

• It equals 1

• It equals -1

• It equals 0

What is the tangent of pi radians?

• -1

• Undefined

• 1

• 0

Why is it useful to define trigonometric functions using the unit circle?

• It simplifies calculations

• It allows for angles greater than 90 degrees

• It eliminates the need for radians

• It makes drawing triangles easier