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Unformatted text preview: ctan(−3). Since −3 < 0, − π < arctan(−3) < 0, so multiplying through by 2 tells us 2 −π < 2 arctan(−3) < 0 which is not in the range [0, 2π ). Hence, we discard this answer along with all other answers obtained for k < 0. Starting with the positive integers, for k = 1 we find x = 2 arctan(−3) + 2π . Since −π < 2 arctan(−3) < 0, we get that x = 2 arctan(−3) + 2π is between π and 2π , so we keep this solution. For k = 2, we get x = 2 arctan(−3) + 4π , and 3 1 The reader is encouraged to see what happens if we had chosen the reciprocal identity cot(3x) = tan(3x) instead. The graph on the calculator appears identical, but what happens when you try to find the intersection points? 4 Geometrically, we are finding the measures of all angles with a reference angle of π . Once again, visualizing these 3 numbers as angles in radian measure can help us literally ‘see’ how these two families of solutions are related. 732 Foundations of Trigonometry since 2 arc...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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