Understanding the Unit Circle and Sine Graphs

This video tutorial explores the unit circle and its application in forming sine and cosine graphs. It begins with a review of the unit circle and trigonometric functions, focusing on how sine and cosine relate to the circle's coordinates. The tutorial then demonstrates how to plot the sine curve by using angles and their corresponding y-coordinates on the unit circle. It covers both positive and negative values, completing the sine curve. The video concludes with a brief introduction to plotting the cosine curve, setting the stage for further exploration.

What is the relationship between the x and y coordinates on the unit circle?

• x is sine, y is cosine

• x is tangent, y is sine

• x is cosine, y is sine

• x is sine, y is tangent

How do you determine the sine value for an angle using the unit circle?

• By finding the y-coordinate

• By finding the tangent

• By finding the x-coordinate

• By finding the hypotenuse

At 90 degrees, what is the sine value?

• 0.5

• -1

• 1

• 0

What happens to the sine value as the angle moves into the third quadrant?

• It becomes positive

• It becomes zero

• It becomes negative

• It remains the same

What is the sine value at 180 degrees?

• 1

• 0

• -1

• 0.5

At 270 degrees, what is the sine value?

• -1

• 0.5

• 1

• 0

What is the significance of the unit circle in forming the sine graph?

• It provides the x-coordinates

• It provides the y-coordinates

• It helps find the tangent values

• It is used to find the hypotenuse

How can the cosine graph be derived from the unit circle?

• By using the tangent

• By using the hypotenuse

• By using the y-coordinate

• By using the x-coordinate

What is the sine value at 360 degrees?

• 1

• 0

• -1

• 0.5

What is the pattern of the sine graph as it completes one full cycle?

• It remains constant

• It increases linearly

• It oscillates between -1 and 1

• It decreases linearly