PRE CALC Name______
Trig Applications Day 2 Solverson
1) One day at summer camp, Paige swung on a rope tied to a tree branch, going back and forth alternately over land and water. Jack started a stopwatch and noticed that when t = 2 seconds, Paigeis at one end of her swing,-23 feet from the river bank and then whent = 5 seconds, she is then at the other end of her swing, 17 feet from the riverbank. (See picture) Assume that while she is swinging, y varies sinusoidally with t.
a) Sketch the graph of y versus t and write the particular equation(label your axes).
b) Write the particular equation expressing y in terms of t.
c) Find y when t = 8.2 seconds. WasPaige over land or over water at this time?
d) What is the first positive value of t at which Paige was directly over the river bank? At that time, was she getting ready to go out over the water or come in over the land? How can you tell?
2. A portion of a roller coaster track is to be built in the shape of a sinusoid. You have been hired to calculate the lengths of the horizontal and vertical timber supports to be used. The high and low points on the track are separated by 50 meters horizontally and 30 meters vertically. The low point is 3 meters below ground. Let y be the number of meter the track is above the ground. Let x be the number of meters horizontally from the start of the ride. Assume that you board the roller coaster at the middle of its vertical height and begin travelling upward.
a) Sketch a graph of this sinusoid.
b) Write an equation expressing y in terms of x.
c) How long is the vertical timber at the high point? When x = 4 meters?
d) Where does the track first hit 25 meters high.go below ground?
D. After you start your stop watch, at what time will point P be at the water's surface? (HINT: See examples from class!)
1.5) For several hundred years, astronomers have kept track of the number of solar flares or “sunspots” that occur on the surface of the Sun. The number of sunspots in a given year varies periodically, from a minimum of about 10 per year to a maximum of about 110 per year. Between 1750 and 1948 there were exactly 18 complete cycles. In 1750, the number of sunspots was 60. (HINT: How long is one cycle, aka period?)
a. Sketch a graph of this situation (label your axes).
b. What is the period of a sunspot cycle?
c.Find the equation for the number of sunspots per year as a function of the year.
d. Assuming this pattern continues, how many sunspots will there be in the year 2020?