Unformatted text preview: − √ 3), let y = arctan( − √ 3), then tan y = − √ 3 for − π 2 < y < π 2 . Therfore y must be the value − π 3 so that arctan( − √ 3) = − π 3 . Because of the limitations on the respective domains of the inverse trigonometric functions, arcsin(sin x ) does not necessarily equal x , arctan(tan x ) does not necessarily equal x , etc. . . However, sin(arcsin x ) = x , tan(arctan x ) = x , etc. . . 1. To ±nd arctan(sin 3 π 4 ), ±rst note 3 π 4 is outside the range of values for y = arcsin x . We have sin 3 π 4 = √ 2 2 . Let y = arcsin(sin 3 π 4 ) = arcsin( √ 2 2 ), or equivalently sin y = √ 2 2 . Therefore y = π 4 and arcsin(sin 3 π 4 ) = π 4 . 2. cos(arccos 1 2 ) = 1 2 since arccos 1 2 = π 3 and cos π 3 = 1 2 . 1...
View
Full Document
 Fall '08
 BANG
 Math, Tan, Inverse function, Inverse trigonometric functions

Click to edit the document details