Unit Circle and Angle Concepts

This video tutorial explains how to find corresponding points on the unit circle for given angles. It covers both positive and negative angles, demonstrating how to sketch angles in standard position and determine where the terminal side intersects the unit circle. The tutorial also highlights the importance of these points in calculating trigonometric function values. Examples include angles like 60, 135, 270, and 210 degrees, as well as negative angles like -60 and -330 degrees. The video emphasizes understanding coterminal angles and their corresponding points on the unit circle.

Why is it important to find the corresponding point on the unit circle for a given angle?

• To measure the circumference of the circle

• To find the length of the radius

• To calculate the area of a circle

• To determine the six trigonometric function values

What is the initial side of an angle in standard position?

• Along the positive x-axis

• Along the negative y-axis

• Along the positive y-axis

• Along the negative x-axis

How do you rotate an angle of 60 degrees from the positive x-axis?

• Clockwise

• Counterclockwise

• Vertically

• Horizontally

What is the corresponding point on the unit circle for 135 degrees?

• Zero, negative one

• One half, square root three divided by two

• Negative one half, negative square root three divided by two

• Negative square root two divided by two, square root two divided by two

What is the terminal side of 270 degrees in standard position?

• Along the negative x-axis

• Along the positive y-axis

• Along the positive x-axis

• Along the negative y-axis

What is the corresponding point on the unit circle for 210 degrees?

• One half, square root three divided by two

• Negative square root three divided by two, negative one half

• Zero, negative one

• Square root three divided by two, one half

How do you rotate an angle of negative 60 degrees from the positive x-axis?

• Horizontally

• Clockwise

• Counterclockwise

• Vertically

What is the corresponding point on the unit circle for negative 330 degrees?

• Square root three divided by two, one half

• Zero, negative one

• Negative one half, negative square root three divided by two

• Negative square root two divided by two, square root two divided by two

Which angle is coterminal with negative 225 degrees?

• 60 degrees

• 135 degrees

• 300 degrees

• 30 degrees

What is the corresponding point on the unit circle for negative 225 degrees?

• Zero, negative one

• Negative square root two divided by two, square root two divided by two

• One half, square root three divided by two

• Square root three divided by two, one half