Determine the exact value of \$arcsin( sin( - (3pi)/4))\$.

A) \$ pi/3\$

B) \$ (2pi)/3\$

C) \$ - pi/4\$

D) \$ pi/12\$

Evaluate \$ tan^(-1) (1/5) - tan^(-1) (1/70) + tan^(-1) (1/99) \$.

A) \$ pi \$

B) \$ (3pi)/2\$

C) \$ pi/6 \$

D) \$- pi/4 \$

Find the value of \$sec^(-1) ((-2\sqrt3)/3) + csc^(-1) (- 1)\$.

A) \$ (5pi)/4 \$

B) \$ pi/3\$

C) \$ (3pi)/2\$

D) \$ (7pi)/4 \$

Determine the exact value of \$ cot^(-1) (- \sqrt3) - sin^(-1) (1/2)\$.

A) \$ (2pi)/3\$

B) \$ (3pi)/2\$

C) 0

D) \$ pi/6 \$

Calculate \$ tan^(-1) (0) - tan^(-1) (\sqrt3/3) + cos^(-1) (\sqrt2/2)\$.

A) \$ pi/12\$

B) \$ pi/6 \$

C) \$ pi/3\$

D) \$ pi \$

In a right triangle, the length of the opposite side to an angle is 6 and the length of the hypotenuse is 12. Find the measure of the angle using the inverse sine function.

A) \$ pi/12 \$

B) \$ pi/6 \$

C) \$ pi/4 \$

D) \$ pi/8 \$

Solve the equation: \$ 5cot^(-1)(x) = (5π)/3 \$.

A) \$ (1/\sqrt(3)) \$

B) \$ \sqrt(3) \$

C) \$(\sqrt(3)/3)\$

D) \$ -\sqrt(3) \$

Find the value of \$ tan^(-1)(1/\sqrt3) + cos^(-1)(- 1/\sqrt2) + sin^(-1)(- 1/2) \$.

A) \$ pi/4 \$

B) \$ (5pi)/4 \$

C) \$ (3pi)/4 \$

D) \$ (7pi)/4 \$

If \$ sin^(-1)(x) + sin^(-1)(y) + sin^(-1)(z) = (3pi)/2 \$, then calculate the value of x + y?

A) 5

B) 1

C) 2

D) 6

Prove the identity: \$ tan^(-1)(x) + tan^(-1)(1/x) = π/2 \$.

A) 1

B) 0

C) Not Proved

D) Proved