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

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 Â½)

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 Â½ 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

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

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Find the exact value of the expressions. (We consider in the ...

#### Solution Summary

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