Given the description of a real-world relationship, find the sinusoidal function that models it. The functions in this exercise have a phase (horizontal) shift.
You might need: Calculator

Problem

A pendulum is swinging next to a wall. The distance from the bob of the pendulum to the wall varies in a periodic way that can be modeled by a trigonometric function.
The modeling function has period 0, point, 8 seconds, amplitude 6, space, c, m, and midline H, equals, 15, space, c, m. At time t, equals, 0, point, 2, the bob is at its midline, moving towards the wall.
Find the formula of the trigonometric function that models the distance H between the bob and the wall after t seconds. Define the function using radians.
space, H, left parenthesis, t, right parenthesis, equals
What is the distance from the pendulum to the wall after 0, point, 5 seconds? Round your answer, if necessary, to two decimal places.
space
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
space, c, m