2 315q 7s 300q 270q 4 5s 3s 3 2 x 3 1 2 2 2 2 2 2 1 3

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Unformatted text preview: 3· ¨, ¸ ¨2 2 ¸ © ¹ S 90q 3 120q § 2 2· ¨ ¨ 2,2¸ ¸ © ¹ S 60q 4 S 45q 135q 30q 150q S 180q § 3 1· ¨ ,¸ ¨ 2 2¸ © ¹ 6 § 3 1· ¨ , ¸ 2¹ ©2 7S 6 § 2 2· , ¨ ¸ 2 2¹ © 0q 210q 5S 4 0 360q 1,0 2S 330q 225q 4S 3 240q §1 3· ¨  , ¸ © 2 2¹ 315q 7S 300q 270q 4 5S 3S 3 2 § x § 3 1· ¨ , ¸ © 2 2¹ 2 2· , ¨ ¸ 2¹ ©2 1 3· ¨ , ¸ ©2 2 ¹ 0,1 For any ordered pair on the unit circle x, y : cos T 11S 6 1,0 x and sin T y Example § 5S · cos ¨ ¸ ©3¹ 1 2 § 5S · sin ¨ ¸ ©3¹  3 2 © 2005 Paul Dawkins Inverse Trig Functions Definition y sin 1 x is equivalent to x sin y y cos 1 x is equivalent to x tan 1 x is equivalent to x sin sin 1 x cos y y Inverse Properties cos cos 1 x x cos 1 cos T T tan y Domain and Range Function Domain y y y sin 1 x 1 cos x 1 tan x 1 d x d 1 Range  1 d x d 1 f  x  f  S d yd 2  y sin 1 sin T T x tan tan 1 x tan 1 tan T T Alternate Notation sin 1 x arcsin x S cos 1 x 2 2 0d y dS S x 1 tan x S arccos x arctan x 2 Law of Sines, Cosines and Tangents c E a J D b Law of Sines sin D sin E a b sin J c Law of Tangents a  b tan 1 D  E 2 1 a  b tan 2 D  E Law of Cosines a 2 b 2  c 2  2bc cos D bc bc b2 a 2  c 2  2ac cos E c2 a 2  b 2  2ab cos J ac ac tan 1 E  J 2 tan 1 E  J 2 tan 1 D  J 2 1 tan 2 D  J Mollweide’s Formula a  b cos 1 D  E 2 c sin 1 J 2 © 2005 Paul Dawkins...
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This document was uploaded on 02/02/2014.

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