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Mat 161 - PreCalculus

The Inverse Sine Function. . Consider the function f(x) = sin (x) on its natural domain. We know that it fails the HLT, so it is not 1-1, therefore it is not invertible.. However, if we restrict the domain we can define the inverse of sine.. Def: The inverse sine function, denoted by arcsin or sin

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Mat 161 - PreCalculus

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    1. Mat 161 - PreCalculus The Inverse Trigonometric Functions Sections 5.7

    2. The Inverse Sine Function

    3. The Inverse Sine Function

    4. The Inverse Sine Function

    5. The Inverse Cosine Function

    6. The Inverse Cosine Function

    7. The Inverse Cosine Function

    8. The Inverse Tangent Function

    9. The Inverse Tangent Function

    10. The Inverse Tangent Function

    11. Use Calculators to evaluateThe Inverse Functions

    12. Cancelation Laws for Trigonometric Functions Inverse Properties The sine function and its inverse sin(sin-1 x) = x for every x in [-1,1] sin-1(sin x) = x for every x in [-?/2, ?/2] 2) The cosine function and its inverse cos(cos-1 x) = x for every x in [-1,1] cos-1(cos x) = x for every x in [0, ?] 3) The tangent function and its inverse tan(tan-1 x) = x for every real number x tan-1(tan x) = x for every x in (-?/2, ?/2)

    13. Trigonometric Functions Find the exact value of each expression: cos(cos-1 0.57) sin(sin-1 (-1/4)) tan(tan-1 25) cos-1(cos 2?/3) sin-1(sin 3?/4) tan-1(tan 2?/3)

    14. Trigonometric Functions Find the exact value of each of the following composite expressions. sin(tan-1 1/3) sec(sin-1 (-1/10) csc(cos-1 (-3/5))

    15. Trigonometric Functions Simplify the following composite expressions. Assume x is positive and that the given expression is defined for x. tan(sin-1 (1/x)) cot(tan-1 (3x) sin(cos-1 vx/4)

    16. Trigonometric Functions Reference: Algebra and Functions Blitzer 3rd Edition

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