Identify the solutions to the equation \$ tan(x - pi) + tan(x + pi/4) = 0\$ on the interval \$ - pi/2 le x le pi/2\$.

A) \$ arctan( 1 + \sqrt2)\$ and \$ arccot(1 + \sqrt2)\$

B) \$ arccot( 1 - \sqrt2)\$ and \$ arccot(1 + \sqrt2)\$

C) \$ arctan( - 1 - \sqrt2)\$ and \$ arctan(- 1 + \sqrt2)\$

D) \$ arctan( 1 - \sqrt2)\$ and \$ arctan(1 + \sqrt2)\$

Identify the general solution to the equation:
\$ (4 cosx)/(sinx) + 3/(sin^2 x) = (6 cosx sinx)/(cos^2 x - 1)\$.

A) \$x = arccos (- 3) + kpi, arccos (- 1/3) + kpi\$

B) \$x = arctan (- 3) + kpi, arctan (- 1/3) + kpi\$

C) \$x = arccot (- 3) + kpi, arccot (- 1/3) + kpi\$

D) \$x = arctan ( 3) + kpi, arctan (1/3) + kpi\$

An architect is designing a circular building with a radius of 50 meters. They need to determine the angle subtended by an arc of 20 meters on the circumference of the building. To ensure precision in the design, they want this angle both in degrees and radians.

A) \$31.92^∘\$ and 1.4 radians

B) \$25.92^∘\$ and 0.2 radians

C) \$22.92^∘\$ and 0.4 radians

D) \$21.29^∘\$ and 2.1 radians

Slove the equation on the interval 0 ≤ x < 2π: secx - 1 - tanx = tanx.

A) \$x = 0 , cos^-1(-3/5)\$

B) \$x = 0 , cos^-1(5/3)\$

C) \$x = 0 , cos^-1(- 5/3)\$

D) \$x = 0 , cos^-1(3/5)\$

In triangle ABC, angle A is twice angle B, and angle C is 40 degrees less than angle A. Find the measures of angles A, B, and C in degrees and radians.

A) \$(22pi)/54 ,(11pi)/45, (4pi)/15\$

B) \$(22pi)/45 ,(11pi)/45, (4pi)/15\$

C) \$(22pi)/45 ,(11pi)/54, (4pi)/15\$

D) \$(22pi)/45 ,(11pi)/45, (4pi)/45\$

\$tan^-1((1 + \sqrt(3)) / (3 + \sqrt(3))) + sec^-1 (\sqrt((8 + 4\sqrt(3))/ (6 + 3\sqrt(3))))\$ is equal to:

A) \$pi/3\$

B) \$(3pi)\$

C) \$(2pi)\$

D) \$pi/2\$

A quadrilateral ABCD has sides AB = 10 ft, BC = 12 ft, CD = 8 ft, and angle B = 60 degrees. Diagonal AC divides the quadrilateral into triangles ABC and ACD. Find side AC.

A) 12.3 ft

B) 14.3 ft

C) 13.3 ft

D) 11.13 ft

A satellite communication company is calibrating a new dish to improve signal reception. The dish needs to be precisely aimed. First, it must be pointed at an angle of 45 degrees to lock onto a satellite in the eastern sky. Later, for a satellite in the western sky, the dish needs to be adjusted to 270 degrees. The angles must be converted to radians for the dish’s motor control system.

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

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

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

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

The light from a lighthouse can be seen from an 18-mile radius. A boat is anchored so that it can just see the light from the lighthouse. A second boat is located 25 miles away from the lighthouse and is headed straight toward it, making a 44º angle with the lighthouse and the first boat. Find the distance between the two ships when the second boat enters the radius of the lighthouse light.

A) 13.8 miles

B) 18.3 miles

C) 15.8 miles

D) 19.8 miles

Considering only the principal values of the inverse trigonometric functions, the value of \$3/2 cos^-1\sqrt(2/(2 + (pi)^2)) + 1/4 sin^-1 ((2\sqrt(2pi))/ (2 + (pi)^2)) + tan^-1 (\sqrt(2)/pi)\$?

A) 2.63

B) 3.62

C) 3.26

D) 2.36