Find all possible solutions of cos(2theta)=3 sin theta-4

Question

a boat leaves port and sails 26 miles at a bearing of S 72 degree 25' E, then turns and sails 32 miles at a bearing on N 17 degree 35' E. How far is the boat from port and what bearing should it follow to sail directly back to the port? Round your answers to the nearest mile and degree.

Answer 1

if cos2T = 3sinT -4

then, because cos2T = cos^2(T)- sin^2(T) = 1-2sin^2(x)

1 - sin^2(T) = 3sinT - 4

sin^2(T) +3sinT- 5 = 0

let x = sinT

x^2 +3x -5 = 0

x = -3/2 +/-(1/2)sqr(9+20)

x = (-3+/-sqr29)/2

x = about 1.19 or - 4.19

sinT = about 1.19 or -4.19 which is impossible as sines are all within 1 of 0

there may be a misprint, miscopy, typo or other problem with the problem

sometimes the problem is figuring out what the problem is

change one sign or one digit by 1 and the problem is solvable