SOLUTION: sin(theta) + cos(theta) = sqrt(2) Solve on the interval of [0,2pi)

Algebra ->  Trigonometry-basics -> SOLUTION: sin(theta) + cos(theta) = sqrt(2) Solve on the interval of [0,2pi)      Log On


   

Question 921832: sin(theta) + cos(theta) = sqrt(2) Solve on the interval of [0,2pi)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
sin(theta) + cos(theta) = sqrt(2) Solve on the interval of [0,2pi)
sinx+cosx=√2
square both sides:
sin^2x+2sinxcosx+cos^2x=2
sin^x+cos^2x=1
2sinxcosx=sin2x
sin^2x+2sinxcosx+cos^2x=2
sin2x+1=2
sin2x=1
2x=π/2
x=π/4