Understanding the Unit Circle

This video tutorial covers the unit circle, a fundamental concept in trigonometry. It explains the unit circle's properties, including its center and radius, and how to navigate it using quadrants. The tutorial introduces reference triangles and demonstrates how to use trigonometric functions like sine, cosine, and tangent to find coordinates on the unit circle. It also emphasizes the importance of memorizing key points from special right triangles, such as 30-60-90 and 45-45-90 triangles, to aid in understanding and solving problems related to the unit circle.

What is the radius of the unit circle?

• 3

• 2

• 1

• 0

In which direction do we rotate around the unit circle?

• Clockwise

• Counter-clockwise

• Horizontally

• Vertically

What is the degree measure when you have completed half of the unit circle?

• 180 degrees

• 270 degrees

• 360 degrees

• 90 degrees

What is the hypotenuse of a reference triangle in the unit circle?

• 2

• 0

• 0.5

• 1

If the angle in a reference triangle is 56 degrees, what trigonometric function would you use to find the vertical side?

• Cosine

• Tangent

• Sine

• Secant

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

• Radius

• Angle

• X-coordinate

• Y-coordinate

How do you calculate the tangent of an angle using coordinates on the unit circle?

• X+Y

• X*Y

• Y/X

• X/Y

What is the radian measure for a 30-degree angle?

• π/2

• π/6

• π/4

• π/3

What are the coordinates for a 45-degree angle on the unit circle?

• (√3/2, 1/2)

• (1/2, √3/2)

• (√2/2, √2/2)

• (1, 0)

Which special triangle is associated with a 60-degree angle?

• 90-90-90

• 45-45-90

• 60-60-60

• 30-60-90