# Trigonometry Application Word Problems - Tire Wear, Trigonometric Equations and Identities

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You interviewed an employee of an association representing the tire industry. The federal government mandates safety testing of all tires manufactured in the United States. Recently there has been concern that the rubber used in the tires could deteriorate while in store inventories. In September 2003, a safety group asked the U.S. government to require expiration dates for tires. Representatives for the manufacturing industry test the tires, collect data and create graphs of functions to test tire durability. As part of the interviewing process, you try to solve the following problems.

1) Two cars with new tires are driven at an average speed of 60 mph for a test drive of 2000 miles. The diameter of the wheels of one car is 15 inches. The diameter of the wheels of the other car is 16 inches. If the tires are equally durable and differ only by diameter, which car will probably need new tires first? Why?

2) Explain why tan(x + 450 degrees) cannot be simplified using the tangent sum formulas, but can be simplified by using the sine and cosine formulas.

3) What is the difference between a trig equation that is an identity and a trig equation that is not an identity? Provide an example to clarify.

It is extremely important for you to show your work. This helps me immensely, as I am much better working backwards when it comes to math problems and solutions.

Thanks

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##### Solution Summary

In this solution, various trigonometry based application word problems and Identities are investigated. The solution is detailed and well presented in an attached Word document.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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