# finding an anglewhat is the x angle if 2sin2x+square root 2=0?

### 2 Answers | Add Yours

We have to solve 2*sin 2x + sqrt 2 = 0

2*sin 2x + sqrt 2 = 0

=> 2*sin 2x = -sqrt 2

=> sin 2x = -1/sqrt 2

2x = arc sin (-1/sqrt 2)

=> 2x = -45 and -135

x = -45/2 + n*180 and x = -135/2 + n*180

We'll move the numer alone to the right side:

2sin 2x = -sqrt2

We'll divide by 2:

sin 2x = -sqrt2/2

2x = (-1)^k*arcsin (-sqrt2/2) + kpi

2x = -pi/4 + kpi

We'll divide by 2:

x = -pi/8 + kpi/2

All the angles x = -pi/8 + kpi/2, where k is an integer number, verify the equation 2sin2x+square root 2=0.