Solve the equation sin 4x Squareroot 32 for solutions in th

Solve the equation sin 4x = Squareroot 3/2 for solutions in the interval [0, 2 pi). Lookout station B is located 9 mi due east of station A. The bearing of a fire from A is S11 degree 40\'W and the bearing from B is S27 degree 50\'W. Determine the distance from the fire to B (to the nearest tenth of a mile).

Solution

sin 4x=sqrt3/2

Taking sin^-1 both sides

4x= sin^-1(sqrt3/2)

4x= pi/3,2pi/3, 7pi/3,8pi/3, 13pi/3, 14pi/3, 19pi/3,20pi/3

x=pi/12,2pi/12,7pi/12,8pi/12,13pi/12,14pi/12,19pi/12,20pi/12

= pi/12, pi/6,7pi/12,2pi/3, 13pi/12, 7pi/6, 19pi/12, 5pi/3