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Unformatted text preview: Trigonometric Functions of Real Numbers What We Know For a circle of radius r , a central angle measured in radians subtends an arc whose length s is r s = If the circle is the unit circle, then r = 1 , so we get = s Agreement Let t be a nonnegative real number. By measuring an arc of length t counterclockwise around the unit circle, we can associate with t a positive angle in standard position that measures t radians . If t is a negative real number, measuring an arc of length  t  clockwise associates with t a negative angle in standard position that measures t radians. (0, 1) (1, 0) (0, 1) (1, 0) t s = t = y x t (0, 1) (1, 0) (0, 1) (1, 0)   t s = t = y x < t Let t be a real number and let P = ( a , b ) be the point on the unit circle that corresponds to t . The sine function associates with t the ycoordinate of P and is denoted by sin t b = The cosine function associates with t the xcoordinate of P and is denoted by cos t a = The tangent function is denoted by tan t and it is defined as , tan = a a b t The cotangent function is denoted by cot t and it is defined as , cot = b b a t The...
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 Fall '08
 GARDNER
 Calculus, PreCalculus, Real Numbers, Unit Circle

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