Answer the given questions about the indicated examples of this section.

In Example 2, if (4, 3) replaces (3, 4), what are the values?

Data from Example 2

Find the values of the trigonometric functions of the standard-position angle θ with its terminal side passing through the point (3, 4).

By placing the angle in standard position, as shown in Fig. 4.13, and drawing the terminal side through (3, 4), we find by use of the Pythagorean theorem that

Using the values x = 3, y = 4, and r = 5, we find that

We have left each of these results in the form of a fraction, which is considered to be an exact form in that there has been no approximation made. In writing decimal values, we find that tan θ = 1.333 and sec θ = 1.667, where these values have been rounded off and are therefore approximate.

r = 3 +4 = 25 = 5