Understanding the Unit Circle

The video tutorial introduces the unit circle, a circle with a radius of one, and explains its significance in trigonometry. It covers how angles are represented on the unit circle and how the cosine and sine functions relate to the x and y coordinates of points on the circle. An example calculation is provided to demonstrate finding coordinates using cosine and sine. The video also explores angles beyond 90 degrees and their effects on sine and cosine values, using animations to illustrate these concepts. Additionally, it introduces the tangent function and wave patterns associated with trigonometric functions. The tutorial concludes with a call to action for viewers to subscribe and engage with the content.

What is the radius of a unit circle?

• 1

• 3

• 0

• 2

What does the term 'unit' in unit circle refer to?

• Infinity

• Zero

• Negative

• Unity

On which plane is the unit circle drawn?

• Polar

• Cartesian

• Spherical

• Cylindrical

What is the significance of theta in the unit circle?

• It represents the radius

• It represents the diameter

• It represents an angle

• It represents a point

In the unit circle, what does the x-coordinate represent?

• sin(theta)

• cos(theta)

• tan(theta)

• cot(theta)

In the unit circle, what does the y-coordinate represent?

• cot(theta)

• sin(theta)

• cos(theta)

• tan(theta)

What is the relationship between the hypotenuse and the radius in a unit circle?

• Hypotenuse is zero

• Hypotenuse is half the radius

• Hypotenuse is twice the radius

• Hypotenuse equals the radius

If theta is 40 degrees, what is the approximate x-coordinate on the unit circle?

• 0.766

• 0.866

• 0.966

• 0.666

If theta is 40 degrees, what is the approximate y-coordinate on the unit circle?

• 0.543

• 0.643

• 0.743

• 0.843

What happens to the sine value as the angle approaches 90 degrees?

• It decreases

• It remains constant

• It increases

• It becomes negative