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Tire Wear and Diameter; Trigonometric Identities and Equations

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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.

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