Solve the equation on the interval 02pi 2sin2 x6sinx8Solutio

Solve the equation on the interval [0,2pi] 2sin^2 x=6sinx+8

Solution

2sin^2 x=6sinx+8

divide the equation by 2:

sin^2x = 3sinx +4

sin^2x - 3sinx -4 =0

sin^2x - 4sinx +sinx -4 =0

sinx( sinx -4) +1(sinx -4) =0

(sinx +1)(sinx -4) =0

sinx =4 (Neglect this as sin cannot be greater than 1)

sinx +1 =0

sinx = -1 on the interval [ 0, 2pi ]

x = sin^-1(-1)

x = 3pi/2

Solution : x= 3pi/2