Find sin 5 pi6 A 16 B 13 C 12 D Squareroot 22 E Squareroot 3

Find sin (5 pi/6), (A) 1/6; (B) 1/3; (C) 1/2; (D) Squareroot 2/2; (E) Squareroot 3/2; (F) -Squareroot 2/2; (G) 0 (H) -1/2 Find cos^-1(sin(5x/6)). (A) pi/6; (B) -pi/6; (C) pi/4; (D) -pi/4; (E) pi/3; (F) -pi/6; (G) 0; Find sin^-1(sin(5 pi/6)). (A) pi/6; (B) -pi/6; (C) pi/4; (D) -pi/4; (E) pi/3; (F) -pi/4; (G) 5 pi/6 Simplify 1 + csc(theta)/cot(theta) + cos(theta). (A) cot(theta); (B) tan(theta); (C) sec (theta); (D) csc(theta); (E) sin(theta) Find all solutions of cos(theta) = -1/2 in the interval [0 degree, 360 degree). (A) 60 degree, -60 degree; (B) 60 degree, 300 degree; (C) 120 degree, 240 degree; (D) 210 degree, 330 degree; (E) 30 degree, 150 degree; (F) 30 degree, 330 degree Find the exact value of sin(pi/4 + pi/3). (A) Squareroot 2 + Squareroot 6/4; (B) Squareroot 2 - Squareroot 6/4; (C) Squareroot 6 - Squareroot 2/4 (D) -Squareroot 2 - Squareroot 6/4; (E) Squareroot 2 + Squareroot 6/2 Find the exact value of cos(165 degree). (A) Squareroot 2 + Squareroot 6/4; (B) Squareroot 2 - Squareroot 6/4; (C) Squareroot 6 - Squareroot 2/4 (D)- Squareroot 2 +- Squareroot 6/4; (E) Squareroot 2 + Squareroot 6/2 Find the exact value of cos(2u) if sin(u) = 4/5 and 0

Solution

1. sin (5pi/6)= sin(pi - pi/6)

sin(pi-theta)=sin theta

therefore(pi - pi/6)=sinpi/6=1/2

correct option is c

2. cos^-1(sin 5pi/6)

sin 5pi/6=1/2

cos^-1(1/2)=pi/3

Correct answer is E

3. sin^-1(sin 5pi/6)

sin 5pi/6=1/2

sin^-1(1/2)=pi/6

correct option is A