Understanding Trigonometric Function Transformations

The video tutorial explains how to find the equation of a function using sine or cosine. It begins by analyzing a curve to determine whether to use sine or cosine, focusing on the amplitude, period, and shifts. The tutorial then calculates the parameters a, b, c, and d, considering the midline, maximum, and minimum values. It explains how to calculate the period and use it to find parameter b. Finally, the tutorial formulates the function equation, incorporating all determined parameters.

What is the amplitude of a function if the absolute value of A is given?

• The amplitude is equal to the absolute value of A.

• The amplitude is equal to A.

• The amplitude is equal to 2A.

• The amplitude is equal to A squared.

Which function type is chosen if the function has a maximum value at a certain point?

• Sine function

• Tangent function

• Cosine function

• Exponential function

What does a reflection across the x-axis indicate about the value of A?

• A is undefined.

• A is positive.

• A is zero.

• A is negative.

If a function starts at the midline and has a minimum value, what is the sign of A?

• Undefined

• Negative

• Zero

• Positive

What is the horizontal shift if the function starts at x = 1?

• Left one unit

• Right one unit

• No shift

• Left two units

How do you calculate the period of a function?

• Amplitude divided by 2π

• B divided by 2π

• 2π divided by B

• 2π divided by the amplitude

What is the value of B if the period is 6?

• π/3

• π/6

• 2π

• 3π

What is the final form of the equation if A is -1, B is π/3, and D is 1?

• y = sin(π/3 * (x + 1))

• y = -sin(π/3 * (x - 1))

• y = sin(π/3 * (x - 1))

• y = -sin(π/3 * (x + 1))

What does the value of C represent in the function equation?

• Horizontal shift

• Vertical shift

• Period

• Amplitude

If there is no vertical shift, what is the value of C?

• 1

• Undefined

• 0

• -1