Sine Function Concepts and Applications

This video is lecture 15 of a pre-calculus course, focusing on the graphs of sine functions. It covers the periodic nature of sine and cosine functions, graphing the basic sine function over one period, and identifying key properties such as symmetry and odd function characteristics. The lecture also explains how to find arguments and calculate amplitude, provides a general formula for graphing sine functions, and includes examples of graphing and solving complex problems involving sine functions.

What is the period of sine and cosine functions?

• π

• 4π

• 2π

• π/2

What is the value of sine at 0?

• Undefined

• 0

• 1

• -1

In which quadrants does the sine function increase?

• Quadrant I and II

• Quadrant I and IV

• Quadrant II and III

• Quadrant III and IV

What is the symmetry property of the sine function?

• Even function

• Odd function

• Symmetric about x-axis

• Neither even nor odd

What is the range of the basic sine function?

• [-1, 1]

• [0, 2]

• [0, 1]

• [-2, 2]

How do you find the x-intercepts of a sine function?

• Set x = 1

• Set x = 0

• Set y = 0

• Set y = 1

What is the amplitude of a sine function?

• The maximum value

• The minimum value

• Half the difference between max and min

• The average value

What is the general formula for the period of a sine function?

• 2π/k

• k/2π

• k/π

• π/k

What does the phase shift in a sine function represent?

• Horizontal shift

• Amplitude change

• Vertical shift

• Period change

How do you determine the start of the period for graphing a sine function?

• Set argument = 0

• Set argument = π

• Set argument = 2π

• Set argument = -π