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This 2 page Class Notes was uploaded by Kennith Herman on Friday October 23, 2015. The Class Notes belongs to MA 113 at University of Kentucky taught by Gluesing-Lueerssen in Fall. Since its upload, it has received 13 views. For similar materials see /class/228129/ma-113-university-of-kentucky in Mathematics (M) at University of Kentucky.
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Date Created: 10/23/15
SOME FACTS EVERY STUDENT OF CALCULUS SHOULD KNOW Below are some basic facts from trigonometry that all of us should know Note that in addition to memorizing certain formulae7 you should also understand how to derive consequences of these formulae H F 9 7 U 03 I The de nitions of the sine and cosine functions using the unit circle The identities sin7x isinx and cos cos7x which tell us that sin is an odd function and cos is an even function The de nitions of tan7 cot7 sec and csc in terms of sin and cos The trigonometric functions for the special angles 07 7r67 7r47 7r37 and any angle obtained by adding a multiple of 7r2 The Pythagorean identity sin2 zcos2 z 1 and how to derive the the identities 1 tanzx sec2 z and 1 cot2 z csczx The addition formulae for sin and cos sinx y sins cosy cos sing and cosz y cos cosy 7 sinx siny Consequences of the addition formulae such as the subtraction and the double angle formulae for sin and cos and the co function identities f7r27z cof where f may be sin7 tan and sec Values of the trigonometric functions at special angles t9 cos0 sin0 tan6 cot0 sect csct9 0 1 0 0 unde ned 1 unde ned 7r V3 1 V3 2 3 a T 5 T V2 T 2 1 g g 1 1 3 7r 1 xC Z T 5 T V2 T 2 T g 0 1 unde ned 0 unde ned 1 27r 1 V3 V3 2 3 T T T quot3 T 2 T e 71 1 1 57r V3 1 V3 2 3 T T 5 T Vg T 2 7T 71 0 0 unde ned 71 unde ned 77r V3 1 V3 2V3 T T 5 T V2 2 T 1 1 w w 47r 1 V3 V3 2V3 3 7 T V2 T 2 T 37quot 0 71 unde ned 0 unde ned 71 57r 1 V3 V3 2 3 3 5 T Vg T 2 T 77r T T T 1 T 2 V2 117r 3 1 3 2 3 T 4 w T 2