Trig Graphs & Transformations

What is the equation of a cosine function with amplitude 2, period 2π, and vertical shift 3?

• y = 2\text{cos}(x) + 3

• y = 3\text{cos}(2x) + 2

• y = 2\text{cos}(x - 3)

• y = 2\text{cos}(x) - 3

What is the difference between sine and cosine functions?

• Sine functions start at the midline (0) and go up, while cosine functions start at the maximum value (amplitude) and go down.

• Sine functions start at the maximum value (amplitude) and go down, while cosine functions start at the midline (0) and go up.

• Both sine and cosine functions start at the midline (0) and oscillate between -1 and 1.

• Sine functions are always positive, while cosine functions can be negative.

What is a vertical shift in a trigonometric function?

• A vertical shift is represented by 'd' in the function y = a*sin(bx - c) + d. It moves the graph up or down on the y-axis.

• A vertical shift is represented by 'a' in the function y = a*sin(bx - c) + d. It stretches the graph vertically.

• A vertical shift is represented by 'b' in the function y = a*sin(bx - c) + d. It compresses the graph horizontally.

• A vertical shift is represented by 'c' in the function y = a*sin(bx - c) + d. It reflects the graph across the x-axis.

What is the phase shift in the function y = a*sin(bx - c) + d?

• c/b

• b/c

• a/d

• d/a

What is the equation of a sine function that has a phase shift of π/2 to the right?

• @@y = ext{sin}(x - rac{ ext{π}}{2})@@

• @@y = ext{sin}(x + rac{ ext{π}}{2})@@

• @@y = ext{sin}(x)@@

• @@y = ext{sin}(x - ext{π})@@

What is the equation for a sine function with an amplitude of 4, period π, and no vertical shift?

What does the amplitude of a trigonometric function represent?

• The distance from the midline to the peak of the graph.

• The frequency of the wave in the function.

• The phase shift of the function.

• The period of the function.

How do you identify the vertical shift in the function y = a*sin(bx - c) + d?

• The vertical shift is represented by 'b'.

• The vertical shift is represented by 'c'.

• The vertical shift is represented by 'd'.

• The vertical shift is represented by 'a'.

What is the equation of a cosine function with a vertical shift of -1 and an amplitude of 5?

What is the general form of a sine function?

• y = a*sin(bx - c) + d

• y = a*cos(bx - c) + d

• y = a*tan(bx - c) + d

• y = a*sin(bx + c) + d