Exploring the Unit Circle and Trigonometric Functions

The video expands the definitions of trigonometric functions, such as sine, cosine, and tangent, to apply to all angles using the unit circle. It explains how these functions are traditionally defined in right triangles and extends these definitions to angles greater than 90 degrees by using the unit circle. The video also covers how the coordinates on the unit circle represent cosine and sine values and discusses how these values change in different quadrants.

What is the purpose of expanding trigonometric functions beyond 90 degrees?

• To simplify calculations

• To apply them to any angle

• To make them more complex

• To limit their usage

What is the significance of the unit circle in trigonometry?

• It helps in defining angles greater than 90 degrees

• It is used to measure angles only

• It simplifies the Pythagorean theorem

• It is only a theoretical concept

Why is the unit circle crucial for defining trigonometric functions for all angles?

• Because it allows for easy computation of angles

• Because it visually simplifies trigonometry

• Because it provides a standard radius

• Because it maps angle measures to coordinates

What is the radius of a unit circle?

• 10 units

• 2 units

• 1 unit

• 0.5 units

In the unit circle, what does the coordinate point represent?

• Cotangent of the angle

• Tangent of the angle

• Secant and cosecant of the angle

• Cosine and sine of the angle

How are the trigonometric functions sine and cosine represented on the unit circle?

• As the sector and segment

• As the diameter and area

• As the radius and circumference

• As the x and y coordinates of a point

What happens to the sine and cosine values in the second quadrant?

• Both are positive

• Cosine is negative, sine is positive

• Cosine is positive, sine is negative

• Both are negative

What is the y-coordinate of a point on the unit circle used to determine?

• The cosine of the angle

• The sine of the angle

• The cotangent of the angle

• The tangent of the angle

In which quadrant are both sine and cosine values negative?

• First Quadrant

• Second Quadrant

• Third Quadrant

• Fourth Quadrant

What does a negative sine value indicate about the angle's position?

• It is in the third or fourth quadrant

• It is less than 90 degrees

• It is in the first or second quadrant

• It is exactly 180 degrees