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Unformatted text preview: 12 Chapter 1 • Right Triangle Trigonometry §1.2 Example 1.10 radicallow 3 3 ◦ A B C D E F radicalBig 3 2 radicalBig 3 2 2 1 45 ◦ Find the sine, cosine, and tangent of 75 ◦ . Solution: Since 75 ◦ = 45 ◦ + 30 ◦ , place a 30 − 60 − 90 right triangle △ ADB with legs of length radicallow 3 and 1 on top of the hypotenuse of a 45 − 45 − 90 right triangle △ ABC whose hypotenuse has length radicallow 3, as in the figure on the right. From Figure 1.2.2(a) we know that the length of each leg of △ ABC is the length of the hypotenuse divided by radicallow 2. So AC = BC = radicallow 3 radicallow 2 = radicalBig 3 2 . Draw DE perpendicular to AC , so that △ ADE is a right triangle. Since ∠ BAC = 45 ◦ and ∠ DAB = 30 ◦ , we see that ∠ DAE = 75 ◦ since it is the sum of those two angles. Thus, we need to find the sine, cosine, and tangent of ∠ DAE . Notice that ∠ ADE = 15 ◦ , since it is the complement of ∠ DAE ....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Trigonometry

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