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    Inverse Trigonometric Functions (15 Problems), Derivatives (7 Problems) and Definite Integrals (8 Problems)

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    7.5 Inverse trigonometric functions

    Find the exact value of the expression.

    1) sin^-1 (SQRT3 / 2)
    2) arctan(-1)
    3) tan^-1 (SQRT 3)
    4) cos^-1 (-1)
    5) csc^-1 (2)
    6) arcsin(-1/ (SQRT 2)
    7) sec^-1 (SQRT 2)
    8) arccos(cos 2pi)
    9) tan^-1 (tan 3pi/4)
    10) cos(arcsin ½)
    11) sin(2 tan^-1 SQRT 2)
    12) cos(tan^-1 (2) + tan^-1 (3))

    Simplify:

    1) tan(sin^-1 (x))
    2) sin(tan^-1 (x)
    3) csc(arctan 2x)

    Find the derivative

    1) y = SQRT(tan^-1 x)
    2) y = tan^-1 SQRT(x)
    3) y = sin^-1(2x+1)
    4) h(x)= SQRT(1-x^2) (arcsin x)
    5) f(x) = xln(arctan x)
    6) y =cos^-1(e^(2x))
    7) y=arctan(cos theta)

    Evaluate the integral

    1) ∫ (from ½ to SQRT3 / 2 on top) [6 / (SQRT(1-t^2))] dt
    2) ∫ (from 0 to 1 on top) [4 / (t^2 + 1)] dt
    3) ∫ (from 0 to SQRT3 / 4 on top) [dx / (1+ 16x^2)]
    4) ∫ (from 0 to 1 / 2 on top) [sin^-1 (x) / (1-x^2)] dx
    5) ∫ [dt / (SQRT(1-4t^2)]
    6) ∫ [6 / (SQRT(1-t^2))] dt
    7) ∫ [tan^-1 (x) / (1+x^2)] dx
    8) ∫ [1 / (x) (SQRT(x^2 - 4))] dx

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    https://brainmass.com/math/integrals/inverse-trigonometric-functions-derivatives-63810

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    Inverse Trigonometric Functions (15 Problems), Derivatives (7 Problems) and Definite Integrals (8 Problems) are solved. The solution is detailed and well presented.

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