How can you solve -2sin2x plus 14sin2x equals 9?

Answer 1

-2sin(2x)+14 sin(2x)=9

12 sin(2x)=9

sin(2x)=9/12

2x= sin^-1(3/4) = sin^-1(0.75)

2x=0.84806 radian

x = 0.42403 radian or 24.295 degrees

The other solution is x=2.7176 radian or 155.705 degrees

Since the sine function has period 2PI, the general solution may be written as

x= 0.43403+ 2nPI, where n is any integer and

x=2.7176 + 2nPI, where n is any integer