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Unformatted text preview: = 0, the formula holds trivially, since tan (sin 1 0) = tan 0 = = 1 2 . Now suppose that 0 < x < 1. Let = sin 1 x . Then is in QI and sin = x . Draw a right triangle with an angle such that the opposite leg has length x and the hypotenuse has length 1, as in Figure 5.3.10 (note that this is possible since < x < 1). Then sin = x 1 = x . By the Pythagorean Theorem, the adjacent leg has length r 1 x 2 . Thus, tan = x 1 x 2 . If 1 < x < 0 then = sin 1 x is in QIV. So we can draw the same triangle except that it would be upside down and we would again have tan = x 1 x 2 , since the tangent and sine have the same sign (negative) in QIV. Thus, tan (sin 1 x ) = x 1 x 2 for 1 < x < 1....
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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, Real Numbers

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