Exploring Sine and Cosine Graphs through the Unit Circle

The video tutorial explains how to generate the graphs of sine and cosine functions using the unit circle. It begins with an introduction to the unit circle and its role in determining the sine and cosine of angles. The tutorial then details the process of graphing y = sin(x) by plotting sine values against angles, showing how the sine function rises and falls. Similarly, it explains graphing y = cos(x) by plotting cosine values, highlighting the function's behavior. Finally, the video compares the sine and cosine graphs, noting their similarities and differences.

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

• The radius of the unit circle

• The length of the terminal arm

• The x-coordinate where the terminal arm intersects the circle

• The y-coordinate where the terminal arm intersects the circle

At what point does the sine function reach its maximum value?

• At 0 radians

• At pi/2 radians

• At pi radians

• At 2pi radians

What is the value of sine at its maximum?

• 0

• -1

• 0.5

• 1

What happens to the sine value after reaching its maximum?

• It remains constant

• It starts to decrease

• It increases further

• It immediately drops to zero

At what value does the sine function reach its minimum?

• 0

• 1

• 0.5

• -1

What is the initial value of cosine at 0 radians?

• 0

• 0.5

• 1

• -1

How does the cosine value change as the angle approaches pi/2 radians?

• It becomes negative

• It decreases to 0

• It remains constant

• It increases to 1

What is the value of cosine at pi radians?

• 1

• -1

• 0

• 0.5

How are the graphs of sine and cosine related?

• They are inverses of each other

• They are phase-shifted versions of each other

• They have no relation

• They are identical

What is the period of the sine and cosine functions?

• 4pi radians

• 2pi radians

• pi/2 radians

• pi radians