sin(x)+cos(x)=1/2

Answer 1

sin^2x+cos^2x = 1

cosx = sqr(1-sin^2x)

sinx + cosx = 1/2

sinx + sqr(1-sin^2x) = 1/2

sqr(1-sinx) = 1/2 - sinx

square both sides to get

1-sin^2x = 1/4 -sinx + sin^2x

2sin^2x - sinx -3/4 = 0

use the quadratic formula to solve for x

x = 1/4 +(1/4)sqr7 = about .91 or -.41