Understanding the Unit Circle by Hand

The video tutorial explains how to construct the unit circle by hand using a unique method involving finger positions to determine cosine and sine values for angles in the first quadrant. It then extends this method to cover the entire unit circle by using symmetry and folding techniques. The tutorial also discusses the signs of coordinates in different quadrants and provides a step-by-step guide to labeling angles around the circle.

What is the primary purpose of using your hand in learning the unit circle?

• To memorize the unit circle

• To draw the unit circle accurately

• To find values in the first quadrant

• To calculate angles precisely

Which finger represents the 45° angle when using your hand to find unit circle values?

• Ring finger

• Middle finger

• Pinky

• Thumb

How do you determine the sine value for a 30° angle using your hand?

• Fold the middle finger and count the fingers

• Fold the ring finger and count the fingers

• Fold the pinky and count the fingers

• Fold the thumb and count the fingers

What is the cosine value for a 60° angle using the hand method?

• √2/2

• √3/2

• 1/2

• 0

In the second quadrant, what happens to the signs of the coordinates?

• First is positive, second is negative

• Both are positive

• Both are negative

• First is negative, second is positive

What is the ordered pair for the angle 180° on the unit circle?

• (0, -1)

• (1, 0)

• (-1, 0)

• (0, 1)

How are the coordinates in the third quadrant determined?

• By mirroring the first quadrant

• By mirroring the second quadrant

• By folding along the x-axis

• By folding along the y-axis

What is the sign of the cosine value in the fourth quadrant?

• Positive

• Negative

• Undefined

• Zero

How much do the angles increase by between the main axes on the unit circle?

• 10°

• 15°

• 30°

• 45°

What is the angle measure for a full rotation around the unit circle?

• 90°

• 360°

• 270°

• 180°