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PP Section 7.1

# PP Section 7.1 - Trigonometric Functions of Real Numbers...

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Trigonometric Functions of Real Numbers

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What We Know For a circle of radius r , a central angle θ measured in radians subtends an arc whose length s is θ r s = If the circle is the unit circle, then r = 1 , so we get θ = s
Agreement Let t be a non-negative 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.

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(0, 1) (-1, 0) (0, -1) (1, 0) t s = t = θ y x 0 t
(0, 1) (-1, 0) (0, -1) (1, 0) | | t s = t = θ y x 0 < t

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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 y -coordinate of P and is denoted by sin t b = The cosine function associates with t the x -coordinate of P and is denoted by cos t a =
The tangent function is denoted by tan t and it is defined as 0 , tan = a a b t The cotangent function is denoted by cot t and it is defined as 0 , cot = b b a t

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PP Section 7.1 - Trigonometric Functions of Real Numbers...

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