Understanding the Unit Circle Concepts

This video tutorial explains how to use sine, cosine, and tangent to determine ordered pairs on the unit circle. It builds on a previous introduction to the unit circle, discussing the triangle's base and height, and the hypotenuse, which is the radius of the unit circle. The video then delves into the trigonometric functions: sine, cosine, and tangent, explaining their relationships to the sides of the triangle and their representation as ordered pairs on the unit circle.

What is the primary purpose of using sine, cosine, and tangent in the context of the unit circle?

• To measure the diameter of the circle

• To find the circumference of the circle

• To calculate the area of the circle

• To determine the ordered pairs on the unit circle

In the context of the unit circle, what does the base of the triangle represent?

• The y-coordinate of the ordered pair

• The x-coordinate of the ordered pair

• The diameter of the circle

• The radius of the circle

Why is it important to understand the base and height of the triangle in the unit circle?

• To measure the diameter of the circle

• To calculate the area of the triangle

• To determine the ordered pairs

• To find the circumference of the circle

What is the length of the hypotenuse in a unit circle?

• Always 1

• Depends on the angle

• Equal to the radius

• Equal to the diameter

What is the significance of the unit circle having a radius of 1?

• It changes the angle measurements

• It makes the circle larger

• It simplifies the calculation of trigonometric functions

• It affects the color of the circle

What does the hypotenuse represent in the context of the unit circle?

• The diameter of the circle

• The radius of the circle

• The x-coordinate of the ordered pair

• The y-coordinate of the ordered pair

What does the term 'sohcahtoa' help us remember?

• The order of operations in trigonometry

• The formulas for area and circumference

• The relationships between the sides of a triangle

• The properties of a circle

How is the sine of an angle in the unit circle defined?

• As the x-coordinate of the ordered pair

• As the radius of the circle

• As the hypotenuse of the triangle

• As the y-coordinate of the ordered pair

What is the relationship between the sine of an angle and the y-coordinate in the unit circle?

• They are equal

• There is no relationship

• Sine is twice the y-coordinate

• Sine is half the y-coordinate

What does the cosine of an angle in the unit circle represent?

• The x-coordinate of the ordered pair

• The y-coordinate of the ordered pair

• The hypotenuse of the triangle

• The radius of the circle