22Chapter 1•Right Triangle Trigonometry§1.324.In Example 1.10 in Section 1.2, we found the exact values of all six trigonometric functions of75◦. For example, we showed that cot 75◦=radicallow6−radicallow2radicallow6+radicallow2. So since tan 15◦=cot 75◦by the CofunctionTheorem, this means that tan 15◦=radicallow6−radicallow2radicallow6+radicallow2. We will now describe another method for finding theexact values of the trigonometric functions of 15◦. In fact, it can be used to find the exact valuesfor the trigonometric functions ofθ2when those forθare known, for any 0◦<θ<90◦. The methodis illustrated in Figure 1.3.5 and is described below.60◦30◦15◦7.5◦OQ1ABCPFigure 1.3.5Draw a semicircle of radius 1 centered at a pointOon a horizontal line. LetPbe the point on thesemicircle such thatOPmakes an angle of 60◦with the horizontal line, as in Figure 1.3.5. Drawa line straight down fromPto the horizontal line at the pointQ. Now create a second semicircle
This is the end of the preview.
access the rest of the document.