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

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

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

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

h(x)

Where are the pictures to understand this question? we can’t you if you don’t show the graphs.

4038 is the answer lol just use a calculator