Question

Trig questions:
What sine function represents an amplitude of 1, a period of 2π, a horizontal shift of π, and a vertical shift of −4?

1. f(x) = sin (x − π) − 4
2. f(x) = sin (πx) + 4
3. f(x) = sin (x + pi over 2) + 4
4. f(x) = sin (pi over 2x) − 4

Paul has a tack stuck in his four-wheeler tire. If the tire has a diameter of 36 inches, how far does the tack travel in 62° of rotation?

1. 31π
2. 18π
3. 31 pi over 5
4. 31 pi over 90

Answer 1

Question 1
Because the period is 2π, and the amplitude is 1obtain
f(x) = sin(x)
Because the horizontal shift is π, obtain
f(x) = sin(x - π)
Because the vertical shift is -4, obtain
f(x) = sin(x - π) - 4

Answer: 1. f(x) = sin(x - π) - 4

Question 2
The radius is 36/2 = 18 in.
1 revolution (360°) is the circumference, which is
2π(18) = 36π in
When the revolution is 62°, the distance traveled is
(62/360)*(36π) = (31/5)π in

Answer: 3. (31π)/5

Question 3.
Consider f(x) = 3cos(2x-π) - 1
f(0) = 3cos(-π) - 1 = -4
f(π/2) = 3cos(0) - 1 = 2
Rate of change = (2+4)/(π/2) = 12/π

From the graph, the rate of change of g(x)  is
3/(π/2) = 6/π

Consider h(x) = sin(x) - 4
h(0) = 0 - 4 = -4
h(π/2) = 1 - 4 = -3
Rate of change = (-3+4)/(π/2) = 2/π
Therefore h(x) has the smallest rate of change

Answer: h(x)