UNIT 6 – Trigonometric Functions
HIGH DIVE Activity Wrap-up
Name: ________________________
Per.: _______ Date: ____________
All Answers Should Be Recorded in Your Notes
Not so Spectacular
The circus owner decided that to save money, he would fill in for the diver from
time to time.
This did not end up being a very good idea because the owner was not an
experienced diver, so he could not safely fall large distances. In fact, he refused
to be dropped from more than 25 feet above the ground. He also insisted that
there would be a huge tub of water under him at all times.
Your task is to find all possible times when the owner will be 25 feet from the
ground. You may want to describe the complete set of possibilities by writing an
algebraic expression for t.
Reminder: Here are the basic facts about the Ferris wheel.
 The radius is 50 feet.
 The center of the Ferris wheel is 65 feet off the ground.
 The Ferris wheel turns counterclockwise at a constant angular speed,
with a period of 40 seconds.
 The Ferris wheel is at the 3 o’clock position when it starts moving.
A Practice Jump
After some not-so-high practice dives by the circus owner, the circus decided to do a practice run of
the show with the diver himself. But they decided to set it up so that they would not have to worry
about a moving cart.
Instead the cart containing the tub of water was placed directly under the Ferris wheel’s 11 o’clock
position. As usual, the platform passed the 3 o’clock position at t = 0.
1. How many seconds will it take for the platform to reach the 11 o’clock position?
2. What is the diver’s height off the ground when he is at the 11 o’clock position?
3. What is his x-position in terms of how far he is from the center of the wheel?
4. What other positions could the cart be placed so that the circus owner will dive from the same or
less height?
Putting the Cart Before the Ferris Wheel
What if you could change where the cart started? That might
make things a little easier.
In this assignment, assume that all the facts about the Ferris
wheel and the cart are the same as usual except for the cart’s
initial position.
Suppose the diver is released exactly 25 seconds after the Ferris
wheel began turning from its 3 o’clock position.
1. What is his x-coordinate as he falls?
2. How far will he fall?
3. Assume it takes him 1 second to fall. Where should the cart
start in order to meet the diver?
More Trig Practice
Sand Castles
Shelly loves to build elaborate sand castles at the beach. Her big problem is that her sand castles take a
long time to build, and they often get swept away by the in-coming tide.
Shelly is planning another trip to the beach next week. She decides to pay attention to the tides so that
she can plan her castle building and have as much time as possible.
The beach slopes gradually up from the ocean toward the parking lot. Shelly considers the waterline to
be “high” if the water comes farther up the beach, leaving less sandy area visible. She considers the
waterline to be “low” if there is more sandy area visible on the beach. Shelly likes to build as close to
the water as possible because the damp sand is better for building.
According to Shelly’s analysis, the level of the water on the beach for the day of her trip will fit this
equation: w(t )  20 sin 29t .
In this equation w(t) represents how far the waterline is above or below its average position. The
distance is measured in feet and t represents the number of hours elapsed since midnight.
In the case shown in the accompanying diagram, the water has come up above its average position,
and w(t) is positive.
1) Graph the waterline function for a 24- hour period.
2) a) What is the highest up the beach (compared to its average position) that the waterline will be
during the day? (This is called high tide.)
b) What is the lowest that the waterline will be during the day? (This is called low tide.)
3) Suppose Shelly plans to build her castle right on the average waterline just as the water has moved
below that line. How much time will she have to build her castle before the water returns and destroys
her work?
4) Suppose Shelly wants to build her castle 10 feet below the average waterline. What is the maximum
amount of time she can arrange to have to make her castle?
5) Suppose Shelly decides she needs only two hours to build and admire her castle. What is the lowest
point on the beach where she can build it?
More Beach Adventures
1) After spending some of the day at the beach building sand castles, Shelly
wants to take an evening walk with a friend along the shoreline.
Shelly knows that at one place along the shore, it is quite rocky. At that point,
the rocks jut into the ocean so that in order to pass around them, a person has to
walk along a path that is 14 feet below the average waterline.
Assume that Shelly and her friend don’t want to get their feet wet. Therefore,
they need to take their walk during the time when the waterline is 14 feet or more
below the average waterline.
What is the time period during which they can take their walk?
(Recall that the position of the waterline over the course of the day is given by
the equation w(t )  20 sin 29t , where the distance is measured in feet and t
represents the number of hours elapsed since midnight.)
2) Shelly often finds herself looking for numbers whose sine is a given value. This question asks you to do
the same. Your solutions should be between -360° and 360°. In Questions 2a and 2b, find exact values for
Ө. In Questions 2c and 2d give Ө to the nearest degree.
a) Find three values of Ө other than 15° such that sin Ө = sin 15°.
b) Find three values of Ө such that sin Ө = sin -60°.
c) Find three values of Ө such that sin Ө = 0.5.
d) Find three values of Ө such that sin Ө = -0.71.