If \$ arcsin(x) = pi/6 \$, find \$ cos( arccos (\sqrt3/2) - arcsin( - 1/2))\$.

A) \$ (2\sqrt3)/2\$

B) \$- 1/2\$

C) \$ 1/2\$

D) \$ \sqrt2/2\$

Find the exact value of \$ arctan(1) + arccos( - \sqrt2 / 2)\$.

A) \$ 2pi \$

B) \$ pi/3 \$

C) \$ pi/2 \$

D) \$ pi \$

Solve for x if \$arccos(2x^2 - 1) = pi/3\$.

A) \$ x = 1/2, x = - 1/2 \$

B) \$ x = \sqrt3/2, x = - \sqrt3/2 \$

C) \$ x = (2\sqrt3)/2, x = - (2\sqrt3)/2 \$

D) \$ x = 1/\sqrt2, x = - 1/\sqrt2 \$

Solve for x if \$ tan^(-1) (2x) + tan^(-1) (3x) = pi/4 \$.

A) \$ 1/6\$

B) \$ 2/3\$

C) \$ 1/3\$

D) \$ 1/8\$

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

A) \$ pi/2\$

B) \$ pi \$

C) \$ pi/4\$

D) \$ pi/6\$

A radio tower 120 meters tall casts a shadow 240 meters long on level ground. Find the angle between the top of the tower and the tip of the shadow using the inverse cosecant function.

A) 60°

B) 30°

C) 120°

D) 90°

Find the principal value of \$ "cosec"^(–1)(2) \$.

A) \$ pi/2 \$

B) \$ pi/6 \$

C) \$ pi/12 \$

D) \$ pi \$

If \$ sin(sin^(-1)(1/9)) + cos^(-1)(x) = 1\$, then what is the value of x?

A) \$ 1/2 \$

B) \$ 1/6 \$

C) \$ 1/9 \$

D) \$ 1/8 \$

A boat leaves a harbor and travels east for 15 kilometers. Then, it changes direction and travels due north for another 15 kilometers. What is the bearing of the boat’s new direction relative to its original position?

A) 105°

B) 90°

C) 45°

D) 75°

Find the exact value of \$ tan^(-1)(1) + cot^(-1) (1) \$.

A) \$ pi/6 \$

B) \$ pi \$

C) \$ pi/4 \$

D) \$ pi/2\$