# PP 7.6 - Inverse Trigonometric Functions The Sine Function...

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Unformatted text preview: Inverse Trigonometric Functions The Sine Function • Domain = (-∞, ∞) • Range = [-1, 1] • Period = 2π • NOT one-to-one Need to restrict the domain to have an inverse function. One-to-One Sine Function One to- One 1] [-1, Range ] , [- Domain 2 2 = = π π Definition x y y x x x f x x x f = ⇔ = = = ≤ ≤- =-- ) sin( ) arcsin( ) ( sin ) ( Then . ), sin( ) ( Let 1 1 2 2 π π y = sin(x) y = arcsin(x) The Other Functions ) arctan( ) ( tan ) ( , ), tan( ) ( ) arccos( ) ( cos ) ( , ), cos( ) ( 1 1 2 2 1 1 x x x f x x x f x x x f x x x f = = ⇒ < <- = = = ⇒ ≤ ≤ =---- π π π y = arcccos(x) y = arctan(x) The Other Functions Secant, cotangent, and cosecant can also be redefined with restricted domains in order to get one-to-one functions and then get inverse functions. The restricted domains for these three functions are not standard as for sine, cosine, and tangent, so be careful when working with them. Cancellation Laws 2 2 1 1 , )) (sin( sin 1 1 , )) ( sin(sin π π ≤...
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PP 7.6 - Inverse Trigonometric Functions The Sine Function...

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