sin(x)+cos(x)=2/3
find the value of
sin(x)
square both sides
sin^2 x + 2sinxcosx + cos^2 x = 4/9
1 + sin 2x = 4/9
sin 2x = -5/9
2x = 213.75 or 2x = 326.25
x = 106.87º or x = 163.126º
but since we performed a "squaring" operation we have to verify each answer.
when x = 106.87 , sin106.87 + cos106.87 = .66676.., so that works
but for x= 163.126, the result was -.66676 which is NOT the right side
so sinx = sin106.87 = .9569