Trigonometric Identies and Equations and Tire Wear

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?

The two cars may be driven at the same speed which is an average of 60 mph but they have tires of differing diameter.  The diameter of the wheels of one vehicle is 15 inches which in turn is smaller then the second that has 16 inches.  Thus, the vehicle with the 15 inch diameter tires will revolve more, faster or take more revolutions than that the of second vehicle with 16 inch diameter tires.  So in turn it will need new tires first.


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.


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.