Rotating Angles and Unit Circle

The video tutorial explains how to find corresponding points on the unit circle for given angles. It covers sketching angles in standard position, determining where the terminal side intersects the unit circle, and using these points to find trigonometric function values. The tutorial addresses both positive and negative angles, providing examples and calculations for each. It also includes methods for handling complex angles and converting between radians and degrees.

What is the first step in finding a point on the unit circle for a given angle?

• Label the angle on the unit circle.

• Convert the angle to degrees.

• Sketch the angle in standard position.

• Find the sine and cosine of the angle.

How do you rotate an angle of 3π/4 radians in standard position?

• Clockwise from the positive y-axis.

• Counterclockwise from the positive x-axis.

• Counterclockwise from the negative y-axis.

• Clockwise from the negative x-axis.

What is the corresponding point on the unit circle for an angle of 3π/4 radians?

• (√2/2, √2/2)

• (-1/2, -√3/2)

• (-√2/2, √2/2)

• (√3/2, -1/2)

Which angle corresponds to the point (-1/2, -√3/2) on the unit circle?

• 3π/4 radians

• π/3 radians

• 4/3π radians

• 11/6π radians

What is the degree equivalent of 11/6π radians?

• 300 degrees

• 330 degrees

• 270 degrees

• 240 degrees

How do you rotate an angle of -π/2 radians in standard position?

• Counterclockwise 90 degrees.

• Clockwise 180 degrees.

• Clockwise 90 degrees.

• Counterclockwise 180 degrees.

What is the corresponding point on the unit circle for an angle of -5/3π radians?

• (√3/2, -1/2)

• (1/2, √3/2)

• (0, -1)

• (-1/2, -√3/2)

What is the degree equivalent of -9/4π radians?

• -405 degrees

• -360 degrees

• -315 degrees

• -270 degrees

How many complete rotations are involved in sketching -9/4π radians?

• Two clockwise rotations.

• One counterclockwise rotation.

• One clockwise rotation.

• Two counterclockwise rotations.

What is the corresponding point on the unit circle for an angle of -9/4π radians?

• (√2/2, -√2/2)

• (-√2/2, √2/2)

• (-√2/2, -√2/2)

• (√2/2, √2/2)