**Negative Identities**

What happens when you plug in –x?

**7.13** Evaluate each of the six trigonometric functions for –*x* to generate the negative trigonometric identities.

Consider the graphs of the trigonometric functions that you generate in Chapters 5 and 6. Any graph that is symmetric about the *y*-axis—in other words, the graph is a reflection of itself across the *y*-axis, as though that vertical line were a mirror—is described as an “even function.” If *f*(*x*) is an even function, then *f*(–*x*) = *f*(*x*). You get the same output when a real number and its opposite are substituted into the function.

Of the six trigonometric functions, only two have *y*-symmetric graphs and are, therefore, even functions: cos *x* and its reciprocal sec *x*. Therefore, cos (– ...

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