Exploring Sine and Cosine Function Graphs

This video tutorial covers the graphing of sine and cosine functions, explaining their periodic nature, concavity, and intervals of increase and decrease. It provides a detailed walkthrough of plotting these functions by hand, understanding their properties, and solving advanced problems. The tutorial also includes a practical exercise for viewers to graph the cosine function independently.

What does the vertical displacement of a point on the unit circle represent in the context of the sine function?

• The y-coordinate of the point

• The radius of the circle

• The angle in radians

• The x-coordinate of the point

At what angle does the sine function first reach its maximum value of 1?

• 3 Pi / 2 radians

• 2 Pi radians

• Pi radians

• Pi / 2 radians

Which of the following best describes the period of the sine function?

• 2 Pi radians

• Pi / 2 radians

• 4 Pi radians

• Pi radians

During which interval is the sine function increasing?

• From 3 Pi / 2 to 2 Pi

• From Pi to 3 Pi / 2

• From Pi / 2 to Pi

• From 0 to Pi / 2

What is the concavity of the sine function from 0 to Pi?

• Concave up

• Concave down

• Linear

• Not defined

At which of the following points does the cosine function start?

• At -1

• At 1

• At Pi / 2

• At 0

Which interval shows the cosine function increasing?

• From 3 Pi / 2 to 2 Pi

• From Pi / 2 to Pi

• From Pi to 2 Pi

• From 0 to Pi

What is the concavity of the cosine function from Pi / 2 to 3 Pi / 2?

• Not applicable

• Concave up

• Concave down

• Both concave up and down

In which quadrant does the angle Theta extend when discussing the function G of a equals a s of a?

• First quadrant

• Second quadrant

• Fourth quadrant

• Third quadrant

If Alpha is between Theta and 3 Pi / 2, how does G of Alpha compare to G of Theta?

• Cannot be determined

• G of Alpha is less than G of Theta

• G of Alpha is greater than G of Theta

• G of Alpha is equal to G of Theta