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Trigonometric Functions WORD problems

Ferris Wheel trigonometry word problem

The Ferris wheel at Navy Pier has a diameter of 140 feet. It stands 10 feet off the ground. The wheel has 40 gondolas that seat six passengers each. It takes about 6 minutes for the Navi Pier Ferris wheel to complete one rotation.

Draw a diagram of the Navy Pier Ferris wheel and the boarding platform. Fill in the necessary information. Sketch the graph. Write a cosine equation for your curve. Write a sine equation for your curve.

Answer the following questions:

i. What is the circumference of the wheel?

ii. At what speed is the wheel traveling? Please answer in feet / second.

iii. If you begin your ride at the base of the wheel, what is the height after 1 minute? 4 minutes?

iv. At what approximate time(s) will you reach the following heights?

a) 100 ft

b) 240 ft

v. What is the length of the arc traveled by the Navy Pier Ferris wheel from the 4 o’clock to the 7 o’clock position?

 

Solution to this Trigonometric Function word practice problem is provided in the video below!



 

Roller Coaster trigonometry problem

A portion of a roller coaster 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.

a. 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 the ground. Letting y be the number of meters the track is above the ground and x the number of meters horizontally from the high point, write an equation expressing y in terms of x.

b. How long is the vertical timber at the high point? At x = 4 m? At x = 32 m?

c. Where does the track first go below ground?

 

Solution to this Trigonometric Function example practice problem is provided in the video below!



 

Steamboat trigonometry example word problem

Mark Twain sat on the deck of a river steamboat. As the paddlewheel turned, a point on the paddle blade moved in such a way that its distance, d, from the water’s surface was a sinusoidal function of time. When his stopwatch read 4 seconds, the point was at its highest, 16 feet above the water’s surface. The wheel’s diameter was 18 feet, and it completed a revolution every 10 seconds.

a. Sketch a graph of the sinusoid

b. Write the equation of the sinusoid

c. How far above the surface was the point when Mark’s stopwatch read:

i. 5 seconds

ii. 17 seconds

d. What is the first positive value of time at which the point was at the water’s surface? At that time, was it going into or coming out of the water? Explain.

 

Solution to this Trigonometric Function example word problem is provided in the video below!



 

Temperature trigonometry word problem

The max temperature in Buenos Aires is on January 15 and is 33 degrees Celsius. The minimum temperature is on July 16 (day 197) and is 9 degrees Celsius. (Assume the period is 365 days).

a) Sketch the temperature as a function of time

b) Find the equation for the temperature, T, as a function of time, t.

c) What is the temperature on Mother’s Day, May 10?

d) Give the dates during a one year period when the temperature is below 18 degrees Celsius.

 

Solution to this Trigonometric Function example word problem is provided in the video below!



 

Trigonometric Form of Complex Numbers problems

Complex Number Trigonometric Form Representation problem example

Express the following Complex Numbers in Trigonometric Form:

-12

-8i

2 – 2i

 

Solution to this Complex Number Trigonometric Form Representation practice problem is provided in the video below!



 

Trigonometric Complex Number Product Quotient Power Rectangular Standard Form Representation example question

Find the resulting Complex Number in standard (rectangular) form for the following:

 

 

Solution to this Trigonometric Complex Number Product Quotient Power Rectangular Standard Form Representation practice problem is provided in the video below!



 

Square Roots of a Complex Number example

Find the two Square Roots of

 

 

Solution to this Square Roots of a Complex Number practice problem is provided in the video below!



 

Complex Number Rectangular POLAR Form Conversion example problem

Express the following POLAR Complex Number in Trigonometric and Rectangular Form: 

 

Express the following Rectangular Complex Number in Trigonometric Form and POLAR Form:

5i

 

Solution to this Complex Number Polar Rectangular Form Conversion practice problem is provided in the video below!



 

Complex Number POLAR Product Quotient Power example question

Find the resulting Complex Number in POLAR form for the following:

a) 

 

b) 

 

Find the resulting Complex Number in POLAR and RECTANGULAR (standard) form:

 

Solution to this Complex Number Polar Product Quotient Power practice problem is provided in the video below!



 

POLAR Complex Number Nth Root Theorem example

Find the Four 4th (Fourth) Roots of

 

Solution to this Polar Complex Number Nth Root Theorem practice problem is provided in the video below!



 

Basic Trigonometric Angles and Values problems

Find ANY Known Trigonometric Value by Hand example question

How do you find the values like or or ?

There is a way to use the Unit Circle information and fill out your own Table of Values fast!

All you need is to start with sine function values in the interval [0, ]

Watch the video below with a detailed tutorial and start being a pro at this!

 

Solution to this Basic Trigonometric Function Values practice problem is provided in the video below!



 

Reference Angles problems

Finding Trigonometric Values Using Reference Angles example question

Find the value of the following Trigonometric Expressions using appropriate Reference Angles:

a) sin(120º)

b)

c) tan(-45º)

d)

e) sec(240º)

f)

 

Solution to this Reference Angle practice problem is provided in the video below!



 

Trigonometric Functions problems

Find All Six Trigonometric Functions using Rectangular Coordinates or given Angle example question

a) If t is a point on the unit circle with coordinates , find the six Trigonometric Functions of t

b) Find the six Trigonometric Functions of

 

Solution to this Trigonometric Function practice problem is provided in the video below!



 




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