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Pre-Calc Exam Notes 22

# Pre-Calc Exam Notes 22 - 22 Chapter 1 Right Triangle...

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22 Chapter 1 Right Triangle Trigonometry §1.3 24. In Example 1.10 in Section 1.2, we found the exact values of all six trigonometric functions of 75 . For example, we showed that cot 75 = radicallow 6 radicallow 2 radicallow 6 + radicallow 2 . So since tan 15 = cot 75 by the Cofunction Theorem, this means that tan 15 = radicallow 6 radicallow 2 radicallow 6 + radicallow 2 . We will now describe another method for finding the exact values of the trigonometric functions of 15 . In fact, it can be used to find the exact values for the trigonometric functions of θ 2 when those for θ are known, for any 0 < θ < 90 . The method is illustrated in Figure 1.3.5 and is described below. 60 30 15 7 . 5 O Q 1 A B C P Figure 1.3.5 Draw a semicircle of radius 1 centered at a point O on a horizontal line. Let P be the point on the semicircle such that OP makes an angle of 60 with the horizontal line, as in Figure 1.3.5. Draw a line straight down from P to the horizontal line at the point Q . Now create a second semicircle
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