Filling Out the Unit Circle: Key Concepts and Techniques

This video tutorial teaches how to fill out the unit circle for long-term understanding, not just short-term memorization. It covers filling in quadrantal angles, angles in terms of pi over 6, pi over 4, and pi over 3, and how to apply these in trigonometry and calculus. The tutorial emphasizes recognizing patterns and understanding the coordinates of the unit circle, which are crucial for graphing trig functions, solving trig equations, and understanding trig identities.

Why is learning the unit circle important?

• Only for solving trig equations

• It's not important

• For use in trigonometry and calculus

• Only for passing quizzes

What is the degree measure at the top of the unit circle?

• 360°

• 90°

• 270°

• 180°

What is the radian measure equivalent to 180°?

• π

• 2π

• π/2

• 3π/2

How many radians are in a full circle?

• 2π

• π

• 4π

• π/2

What is the degree measure corresponding to π/6 radians?

• 90°

• 60°

• 45°

• 30°

What is the radian measure for an angle of 45°?

• π/4

• π/2

• π/3

• π/6

What are the coordinates of the point on the unit circle at 0°?

• (-1, 0)

• (0, 1)

• (0, -1)

• (1, 0)

What is the x-coordinate of the point on the unit circle at 90°?

• √2/2

• -1

• 0

• 1

Which quadrant contains the angle measure of 7π/6?

• I

• II

• III

• IV

What is the y-coordinate of the point on the unit circle at 270°?

• 0

• √3/2

• -1

• 1