Question

Use the sliders to change the values of a, b, and c in the sine function. Which equation has a maximum at

−π/4,3 and a minimum at π/4,3?
a) y=−3sin(x−1)
b) y=−3sin(x−2)
c) y=−3sin(2x)
d) y=−3sin(3x)

Answer 1

The equation that has a maximum at −π/4,3 and a minimum at π/4,3 is y=−3sin(x−2).

Step-by-step explanation:

The equation that has a maximum at −π/4,3 and a minimum at π/4,3 is y=−3sin(x−2).

To determine this, we need to consider the x values at which the sine function has its maximum and minimum value. The maximum value of the sine function occurs when the argument of the function is equal to π/2 + 2nπ, where n is an integer. In this case, the maximum occurs at x = −π/4 + 2π = −π/4, and the minimum occurs at x = π/4 + 2π = π/4. Therefore, the equation y=−3sin(x−2) satisfies the given conditions.