Understanding Sine and Cosine Graphs

What is the y-value of y = sin(2x) when x = π/4?

• 1

• -1

• 0.5

• 0

At which x-value does y = sin(2x) return to zero after starting at x = 0?

• π

• π/2

• 2π

• 3π/2

How does the coefficient of x in y = a * sin(bx) affect the period of the function?

• It doubles the period

• It halves the period

• It inverts the period

• It changes the period to 2π/b

What is the period of the function y = -3 * cos(12x)?

• π/6

• π

• 2π

• 4π

What is the amplitude of y = -3 * cos(12x)?

• 6

• -3

• 3

• 1

What does the negative sign in front of a cosine function indicate about its graph?

• It changes the amplitude

• It shifts the graph up

• It reflects the graph over the x-axis

• It changes the period

What is the period of y = (1/4) * sin(3x)?

• π

• π/3

• 2π/3

• 2π

What is the amplitude of y = (1/4) * sin(3x)?

• 3

• 1

• 1/2

• 1/4

How do you find the midpoint between two numbers when graphing trigonometric functions?

• Add them and divide by two

• Multiply them

• Subtract them

• Divide them

What is the first step in sketching a graph once you know the period?

• Plot the x-intercepts

• Cut the period in half

• Double the period

• Find the amplitude