Understanding Trigonometric Functions from a Table of Values

The video tutorial explains how to determine a trigonometric function from a table of values. It begins by plotting the points on a coordinate plane to analyze their behavior, which resembles either a sine or cosine function. The tutorial then focuses on deriving an equation using the cosine function, identifying key parameters such as amplitude, period, and shifts. The process involves calculating the values of A, B, C, and D, which define the function's characteristics. The video concludes by presenting a possible cosine function equation and hints at exploring the sine function in a subsequent video.

What is the first step in determining a trigonometric function from a table of values?

• Calculating the amplitude

• Guessing the function type

• Plotting the points on a coordinate plane

• Analyzing the table of values directly

Which trigonometric functions do the plotted points resemble?

• Secant and Cosecant

• Tangent and Cotangent

• Exponential and Logarithmic

• Sine and Cosine

Why is the cosine function chosen over the sine function in this example?

• The graph starts with a maximum at the y-axis

• The graph is reflected across the x-axis

• The graph starts with a minimum at the y-axis

• The graph has a phase shift

What is the midline of the graph in this example?

• y = 0

• y = 2

• y = -2

• y = -4

How is the amplitude of a trigonometric function determined?

• By finding the distance from the midline to the maximum or minimum

• By calculating the period of the function

• By identifying the phase shift

• By determining the vertical shift

What is the period of the function in this example?

• 4 units

• 6 units

• 8 units

• 10 units

What is the value of B in the function equation?

• π/8

• π/2

• π/4

• π/6

What is the phase shift of the graph?

• 2 units to the left

• 4 units to the right

• 2 units to the right

• No shift

What is the vertical shift of the graph?

• 4 units down

• 2 units down

• 4 units up

• 2 units up

What is the final equation of the cosine function?

• f(x) = 4 cos(π/6 x) + 2

• f(x) = 4 cos(π/6 x) - 2

• f(x) = 6 cos(π/4 x) - 2

• f(x) = 6 cos(π/4 x) + 2