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Pre-Calc Exam Notes 28

# Pre-Calc Exam Notes 28 - 28 Chapter 1 Right Triangle...

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28 Chapter 1 Right Triangle Trigonometry §1.4 Example1.23 x y 0 0 (1 , 0) 90 (0 , 1) 180 ( 1 , 0) 270 (0 , 1) Figure 1.4.6 Find the exact values of all six trigonometric functions of 0 , 90 , 180 , and 270 . Solution: These angles are different from the angles we have con- sidered so far, in that the terminal sides lie along either the x -axis or the y -axis. So unlike the previous examples, we do not have any right triangles to draw. However, the values of the trigonometric functions are easy to calculate by picking the simplest points on their terminal sides and then using the definitions in formulas (1.2) and (1.3). For instance, for the angle 0 use the point (1 , 0) on its terminal side (the positive x -axis), as in Figure 1.4.6. You could think of the line segment from the origin to the point (1 , 0) as sort of a degenerate right triangle whose height is 0 and whose hypotenuse and base have the same length 1. Regardless, in the formulas we would use r = 1, x = 1, and y = 0. Hence: sin 0 = y r = 0 1 = 0 cos 0 = x r = 1 1 = 1 tan 0
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