Trigonometric Functions and Transformations

The video tutorial explains how to find a possible equation for a transformed trigonometric function. It involves sketching a sine or cosine function with the same transformation, determining the equation of that function, and using it to find the equation of the original function. The process includes analyzing graph points, calculating midline, amplitude, period, and phase shift, and verifying the results by graph comparison.

What is the first step in finding a possible equation for the blue trigonometric function?

• Sketch a tangent function.

• Identify it as a transformation of a secant or cosecant function.

• Use a logarithmic function.

• Apply a linear transformation.

How are the relative minimums of the cosecant function related to the sine function?

• They are the midpoints of the sine function.

• They are the minimums of the sine function.

• They are the maximums of the sine function.

• They are unrelated to the sine function.

What is the midline value for the transformed sine or cosine function?

• y = 0

• y = 5

• y = 1

• y = 3

What is the amplitude of the transformed sine function?

• 2

• 5

• 1

• 3

How is the period of the sine function calculated?

• 2π divided by the phase shift

• 2π divided by the vertical shift

• 2π divided by the amplitude

• 2π divided by b

What is the phase shift of the transformed sine function?

• Left 1 unit

• Right 1 unit

• Left 2 units

• Right 2 units

What is the vertical shift of the transformed sine function?

• Up 3 units

• Down 3 units

• Down 1 unit

• Up 1 unit

What is the equation of the transformed sine function?

• y = 2 sin(π/3 (x + 1)) + 3

• y = 2 sin(π/3 (x - 1)) + 3

• y = 2 sin(π/3 (x - 1)) - 3

• y = 2 sin(π/3 (x + 1)) - 3

What is the equation of the original blue cosecant function?

• y = 2 cosecant(π/3 (x + 1)) + 3

• y = 2 cosecant(π/3 (x - 1)) + 3

• y = 2 cosecant(π/3 (x - 1)) - 3

• y = 2 cosecant(π/3 (x + 1)) - 3

How can you verify the equation of the original blue function?

• By comparing it with a tangent graph.

• By checking the equation with a logarithmic function.

• By graphing both functions on the same coordinate plane.

• By using a calculator.