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Section7_5_review - Section 7.5 Inverse Trigonometric...

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Section 7.5: Inverse Trigonometric Functions The inverse tangent function fx ( 29 = tan - 1 x exists for fx ( 29 = tan x , - π 2 < x < π 2 . Note that the domain of fx ( 29 = tan - 1 x is -∞ , ( 29 and the range is - π 2 , π 2 . The inverse sine function fx ( 29 = sin - 1 x exists for f x (29 = sin x , - π 2 x π 2 . Note that the domain of fx ( 29 = sin - 1 x is - 1 ,1 [ ] and the range is - π 2 , π 2 . The inverse cosine function fx ( 29 = cos - 1 x exists for fx ( 29 = cos x , 0 x π . Note that the domain of fx ( 29 = cos - 1 x is - 1 ,1 [ ] and the range is 0, π [ ] . Differentiation/Integration formulas involving the inverse trig. functions: d dx tan - 1 u ( 29 = 1 1 + u 2 du dx d dx sin - 1 u ( 29 = 1 1 - u 2 du dx d dx cos - 1 x ( 29 =- 1 1 - u 2 du dx 1 x 2 + 1 dx = tan - 1 x + c 1 x 2 + a 2 dx = 1 a tan - 1 x a + c 1 1 - x 2 dx = sin - 1 x + c Problem. Differentiate y = cos - 1 3 x 2 ( 29 . Solution. d dx cos - 1 u = - 1 1 - u 2 du dx y = - 1 1 - 3 x 2 ( 29 2 d dx 3 x 2 ( 29 = - 6 x 1 - 9 x 4 Problem. Differentiate f t ( 29 = tan - 1 1 - t .
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