Stitz-Zeager_College_Algebra_e-book

2 starting with the right hand side of tan sin sec

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Unformatted text preview: line around the Unit Circle and associating to each real number t an oriented arc 15 Note that the negative sign indicates clockwise rotation in both systems, and so it is carried along accordingly. 604 Foundations of Trigonometry on the Unit Circle with initial point (1, 0). Viewing the vertical line x = 1 as another real number line demarcated like the y -axis, given a real number t > 0, we ‘wrap’ the (vertical) interval [0, t] around the Unit Circle in a counter-clockwise fashion. The resulting arc has a length of t units and therefore the corresponding angle has radian measure equal to t. If t < 0, we wrap the interval [t, 0] clockwise around the Unit Circle. Since we have defined clockwise rotation as having negative radian measure, the angle determined by this arc has radian measure equal to t. If t = 0, we are at the point (1, 0) on the x-axis which corresponds to an angle with radian measure 0. In this way, we identify each real number t with the corresponding angle with...
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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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