As the use of electricity became widespread in the 1880s, there was a serious debate over the best way to distribute electric power. The American inventor Thomas Edison favored the use of direct current because it was safer and did not vary with time. Another American inventor and engineer, George Westinghouse, favored alternating current because the voltage could be stepped up and down with transformers during transmission.

Also favoring the use of alternating current was Nikola Tesla, an American (born in Croatia) electrical engineer, and he had a strong influence on the fact that alternating current came to be used for transmission. Tesla developed many electrical devices, among them the polyphase generator that allowed alternating current to be transmitted with constant instantaneous power. Using this type of generator, power losses are greatly reduced in transmission lines, which allows for smaller conductors, and the power can be generated far from where it is used. Three-phase systems are used in most commercial electric generators as well as some electric cars, including those produced by Tesla Motors, a company named in honor of Nikola Tesla.

The trigonometric relationships that we develop in this chapter are important for a number of reasons. In fact, we already made use of some of them in Section 10.4 when we graphed certain trigonometric functions, and in Chapter 9 in deriving the law of cosines. In calculus, certain problems use trigonometric relationships, even including some in which these functions do not appear in the initial problem or final answer. Also, they are useful in a number of technical applications in areas such as electronics, optics, solar energy, and robotics.

Later in the chapter, we see that various trigonometric relationships are used in solving equations with trigonometric functions. Also, we develop the concept of the inverse trigonometric functions that were introduced in Chapter 4.