sinx + sqrt2 = -sinx  x belongs to (0,2pi)

Expert Answers
hala718 eNotes educator| Certified Educator

sinx + sqrt2 = -sinx

==> 2sinx + sqrt2 = 0

==> 2sinx = -sqrt2

Divide by 2:

==> sinx = -sqrt2/2

But sin pi/4 = sqrt2/2

We know that the sine is negative in both 3rd and 4th quadrants:

==> x1= pi + pi/4 = 5pi/4

==> x2= 2pi - pi/4 = 7pi/4

neela | Student

To solve sinx+sqrt2 = -sinx

Sinx+sinx = -sqrt2

2sinx = -sqrt2

sinx =-sqrt2/2 = -1/sqrt 2 = sin(180+45) = sin(360-45)

x = 180+45 =225 degree or x= 360-45 = 315 deg

x  = 225  deg or 315 deg