Question

Modeling with an inverse trig function: A bird sits on the branch of a tree, then starts to fly. The height of the bird is described by the function

y=0.6sin( 12πx)+35, where y represents the height of the bird measured in meters, and x represents the number of seconds since the bird left the branch. Which function expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters?
a. y= 12 / π sin ^−1(x−35 / 0.6)
b. y= 12 / π sin ^−1(x+35 / 0.6)
c. y= π/ 12sin ^−1(x / 0.6) -35
d. y= π/ 12sin ^−1(x / 0.6) + 35

Answer 1

The correct function to express time as a function of the bird's height is y = (1/(12π))sin-1((x - 35) / 0.6), which represents the time in seconds since the bird left the branch.

Step-by-step explanation:

The question involves modeling the height of a bird flying as a function of time using a sine wave and then finding the inverse function to express time as a function of height. The original height as a function of time is given by y=0.6sin(12πx)+35. To find the function expressing the number of seconds since the bird left the branch as a function of the height of the bird, y, we will need to solve for x by using the inverse sine function.

First, we must isolate the sine term by subtracting 35 from both sides and then dividing by 0.6:

x = sin-1((y - 35) / 0.6) / (12π)

Therefore, the correct inverse function to express time as a function of height is:

y = (1/(12π))sin-1((x - 35) / 0.6), which corresponds to option a. y= 12 / π sin−1(x−35 / 0.6).