Understanding Trigonometric Functions

The video tutorial explains how to determine an equation for a trigonometric function using a table of values. It covers plotting points on a coordinate plane, identifying sine and cosine functions, sketching the midline, and using the sine function to model the graph. The tutorial also details finding the values of A, B, D, and C, and writing the equation of the sine function. The process is compared to using the cosine function, highlighting differences in phase shift and reflection.

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

• Identify the maximum and minimum values

• Plot the points on a coordinate plane

• Calculate the amplitude

• Determine the period of the function

Which points are plotted on the coordinate plane in the video?

• (0,4), (2,-2), (4,-8), (6,-2), (8,4), (10,-2), (12,-8)

• (0,5), (2,-3), (4,-9), (6,-3), (8,5), (10,-3), (12,-9)

• (0,2), (2,0), (4,-6), (6,0), (8,2), (10,0), (12,-6)

• (0,3), (2,-1), (4,-7), (6,-1), (8,3), (10,-1), (12,-7)

What is the midline of the function based on the maximum and minimum values?

• Y = 2

• Y = -2

• Y = 0

• Y = -4

What is the amplitude of the sine function in the video?

• 4 units

• 8 units

• 6 units

• 10 units

How is the value of B determined for the sine function?

• By determining the horizontal shift

• By solving 2PI divided by B equals the period

• By identifying the vertical shift

• By calculating the distance from the midline to the maximum

What is the phase shift of the sine function in the video?

• Right 4 units

• Left 2 units

• Right 2 units

• Left 4 units

What is the value of C in the sine function equation?

• C = -2

• C = 0

• C = 2

• C = -4

What is the final equation of the sine function derived in the video?

• F(X) = 6 sin(PI/4 (X+2)) + 2

• F(X) = -6 sin(PI/4 (X-2)) - 2

• F(X) = 6 cos(PI/4 (X-2)) + 2

• F(X) = -6 cos(PI/4 (X+2)) - 2

Why is using the cosine function considered more straightforward in the video?

• It has a larger amplitude

• It does not require a phase shift or reflection

• It has a shorter period

• It starts at the midline

What is the significance of the reflection across the X-axis in the sine function?

• It changes the period of the function

• It alters the amplitude

• It indicates the function starts at a minimum

• It affects the vertical shift