the Inverse Property for the Sine function. If 1 1 and then x y sin(arcsin = and arcsin(sin = x) x y) y. the Inverse Property for the Cosine function. If 1 1 and 0 then x y cos(arccos = and arccos(cos = x) x y) y. State the Inverse Property for the Tangent function. If is a real number and < < then x y tan(arctan = and arctan(tan = x) x y) y. Derivatives of Inverse Trigonometric Functions What you should learn (Pages How to differentiate an inverse trigonometric Let be a differentiable function of u x. function [arc secu] [arcsin d = d u] = dx 1 u2 [arccos d u] = dx u2 [arctan d u] 1 + u2 = dx [arc cot d u] 1 + u2 = dx dx | | u 1 u2 [arc cscu] d = | | 1 u u2 dx Homework Assignment
the Inverse Property for the Sine function. If 1 x 1 and y then sin(arcsin x) = x and arcsin(sin y) = y. the Inverse Property for the Cosine function. If 1 x 1 and 0 y then cos(arccos x) = x and arccos(cos y) = y. State the Inverse Property for the Tangent function. If x is a real number and < y < then tan(arctan x) = x and arctan(tan y) = y. Derivatives of Inverse Trigonometric Functions (Pages Let u be a differentiable function of x. What you should learn How to differentiate an inverse trigonometric function d [arcsin u] = dx d [arccos u] = dx d [arctan u] = dx d [arc cot u] = dx d [arc secu] = 1 u2 u2 1 + u2 1 + u2 dx d [arc cscu] = dx | u | | u | u2 1 u2 1 Homework Assignment
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