Explore BrainMass

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

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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) &#8747; (from Â½ to SQRT3 / 2 on top) [6 / (SQRT(1-t^2))] dt
2) &#8747; (from 0 to 1 on top) [4 / (t^2 + 1)] dt
3) &#8747; (from 0 to SQRT3 / 4 on top) [dx / (1+ 16x^2)]
4) &#8747; (from 0 to 1 / 2 on top) [sin^-1 (x) / (1-x^2)] dx
5) &#8747; [dt / (SQRT(1-4t^2)]
6) &#8747; [6 / (SQRT(1-t^2))] dt
7) &#8747; [tan^-1 (x) / (1+x^2)] dx
8) &#8747; [1 / (x) (SQRT(x^2 - 4))] dx

Â© BrainMass Inc. brainmass.com March 4, 2021, 6:49 pm ad1c9bdddf
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.

\$2.49