A sine wave function f(x) = a sin(bx) has amplitude 10 and period 40. What are the

values of a and b?
(A) a = 10 and b = 20/pi (
B) a = 10 and b = 1/40
(C) a = 10 and b = pi/20
(D) a = 10 and b = 40
E) None of the above.

b = 2pi*f*t = 2*pi*1/T = 2pi/T = 2pi/40

= pi/20.
Answer: C.

CORRECTION:

b = 2pi*f = 2pi*1/T = 2pi/T = 2pi/40 =
pi/20.
Answer: C.

Write a sine function that has an amplitude of 4, period of 3π, and midline y = -3

To find the values of a and b for the sine wave function f(x) = a sin(bx) with amplitude 10 and period 40, you can use the given information.

1. The amplitude of a sine function is the absolute value of the coefficient of sin(bx), which in this case is 10. So, a = 10.

2. The period of a sine function is 2π divided by the coefficient of x, which in this case is b. So, the period 40 can be written as 2π/b = 40.

To solve for b, we can rearrange the equation and solve for b:

2π/b = 40

Cross-multiply and solve for b:

2π = 40b

b = 2π/40

Simplifying, we get:

b = π/20

Thus, the values of a and b for the given sine wave function are a = 10 and b = π/20.

Therefore, the correct answer is option (C): a = 10 and b = π/20.