Advanced Functions
posted by Anonymous on .
Determine all solutions in the interval
x is all real numbers , [0, 2 pi]
using a trigonometric identify
2cos^2x + sinx  1 = 0

2cos^2x + sinx  1 = 0
2(1  sin^2x) + sinx  1 = 0
2  2sin^2x + sinx  1 = 
2sin^2x  sinx 1 = 0
(2sinx + 1)(sinx  1) = 0
sinx = 1/2 or sinx = 1
from sinx = 1/2, x = pi + pi/6 or 2pi  pi/6
x = 7pi/6 radians or 11pi/6 radians ,
(210º or 330º)
from sinx = 1, x = pi/4 radians, (90º)