Solve for x in the interval 0 ≤ x < 2π:
\$2 sin^2 (x) − 3 sin(x) + 1 = 0\$.

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

B) \$ pi/6, (5pi)/6, pi/2\$

C) \$ pi/4, (3\pi)/4, \pi/2\$

D) \$ pi/6, (2pi)/3, (3pi)/2\$

A plane is flying at an altitude of 5000 feet. The angle of elevation from the ground to the plane is 20 degrees. How far away horizontally is the plane from the observer?

A) 15122 feet

B) 14000 feet

C) 13736 feet

D) 12281 feet

Solve for x in the interval 0 ≤ x < 2π:
\$cos(2x) + \sqrt(3) cos(x) − 1 = 0\$.

A) \$ (\pi/6), ((5\pi)/6), ((7\pi)/6), ((11\pi)/6)\$

B) \$ (\pi/3), ((2\pi)/3), ((4\pi)/3), ((5\pi)/3)\$

C) \$ (\pi/6), ((5\pi)/6), (\pi), (2\pi)\$

D) \$ (\pi/4), ((3\pi)/4), ((5\pi)/4), ((7\pi)/4)\$

Solve for x in the interval 0 ≤ x < 2π: \$2cos^3 (x) - 3cos^2 (x) + cos(x) = 0\$.

A) \$x = 0, (\pi)\$

B) \$x = (\pi/2), ((3\pi)/2)\$

C) \$x = (\pi/4), ((5\pi)/4)\$

D) \$x = (\pi/3), ((2\pi)/3)\$

Solve for x in the interval 0 ≤ x < 2π:
\$sin(x) + sin(2x) = 0\$.

A) \$0, (\pi), (2\pi), ((2\pi)/3), ((4\pi)/3)\$

B) \$0, (\pi), (2\pi), (\pi/2), ((3\pi)/2)\$

C) \$0, (\pi), (2\pi), (\pi/4), ((5\pi)/4)\$

D) \$0, (\pi), (2\pi), (\pi/3), ((5\pi)/3)\$

Prove that: \$ sin(3x) = 3sin(x) − 4sin^3(x) \$.

A) Proved

B) Not Proved

C) Infinity

D) Zero

Identify the solutions to the equation \$4cos^2 (x - (pi)) = 3\$ on the interval 0 ≤ x < 2π.

A) \$(pi)/6, (5pi)/6, (7pi)/6, (11pi)/6\$

B) \$(pi)/4, (5pi)/6, (7pi)/4, (11pi)/6\$

C) \$(pi)/6, (5pi)/4, (7pi)/6, (11pi)/4\$

D) \$(pi)/2, (5pi)/2, (7pi)/2, (11pi)/2\$

Find all solutions to the equation \$ sin(2x) = cos(x) \$ for 0 ≤ x ≤ 2π.

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

B) \$ pi/6, (5pi)/6 \$

C) \$ pi/2, (5pi)/2 \$

D) \$ pi/2, (5pi)/4 \$

Identify the general solution to the equation: \$(tanx -1) /( tanx + 1) = - 2\$.

A) \$tan^-1(-1/5) + k(pi)\$

B) \$tan^-1(-1/6) + k(pi)\$

C) \$tan^-1(-1/3) + k(pi)\$

D) \$tan^-1(-1/7) + k(pi)\$

Identify the solutions to the below equation on the interval \$ 0 le x < 2pi\$
\$ (4 cos^3 x - 2 cosx)/(cosx) = 0\$.

A) \$ pi/6, (3pi)/6, (5pi)/6, (7pi)/6\$

B) \$ pi/2, (3pi)/4, (5pi)/4, (7pi)/2\$

C) \$ pi/4, (3pi)/2, (5pi)/2, (7pi)/4\$

D) \$ pi/4, (3pi)/4, (5pi)/4, (7pi)/4\$