4.1 Ferris wheel trig problems
Trigonometry can be confusing for some students, most especially, if they don’t know what they could do with these concepts in real life. In studying a topic that you are not completely comfortable with, the best way to cope is to find ways in appreciating it. The more you try to dodge it because you don’t like the idea of learning about it, the more difficult it would be for you to understand. So, let’s try to look at the most applications of the trigonometric functions.
Do you remember that scene in GI Joe Rise of Cobra where they used spherical trigonometry to find out the location of their target guy? They used the shadow and height of the person, and the time and date the picture was taken.
Another example of an application of trigonometric function would be of the most common theme park ride the Ferris wheel. If you want to know how long will be the distance that you would travel after four rounds, then you will use the radius, the approximate length of a round and the height of your seat from the ground.
You can also use trigonometry to find out the best time for you to go surfing, because you can make a trigonometric graph to predict the tides and water depth. It is also applicable for the simple harmonic motion of a spring which is fairly useful in understanding the mechanism of the shock absorbers of your car.
In the previous chapters we were able to talk about sinusoidal function. If you may recall, these are the functions with graphs that oscillate by an amplitude of 1 unit going up and another unit going down for every period of 2$\pi$. This function can be used to make models in predicting certain outcomes or even behavior of a data. For example, a researcher can use the sinusoidal function if he would want to model the population of predators and prey in a pa particular ecosystem, or you can use it if you want to know how to control the thermostat in your house.
There are also a lot of application of the trigonometric functions in astronomy, geometry and trigonometry. The more you try to understand its concepts the more you will see how trigonometry is everywhere around you.
Ferris wheel trig problems
Lessons

a)
Graph how the height h of a passenger varies with respect to the elapsed time t during one rotation of the Ferris wheel. Clearly show at least 5 points on the graph.

b)
Determine a sinusoidal function that gives the passenger’s height, h, in meters, above the ground as a function of time t seconds.

c)
How high above the ground would a passenger be 18 seconds after the Ferris wheel starts moving?

d)
How many seconds on each rotation is a passenger more than 30m in the air?
