Egyenlet megoldása

`sin^2x=a`

`cos^2x=1-a`

`a^2+(1-a)^2` = `5/8`

`2a^2-2a+1=5/8`

`a^2-a+3/16=0`

`a_(1,2)` = `(1 pm root()(1-3/4))/2` = `(1pm1/2)/2`

`a_1` = `1/4` = `sin^2x`

`sinx` = `1/2`

`x_1` = `pi/6+2*k*pi`

`x_2` = `(5*pi)/6+2*k*pi`

`sinx` = `-1/2`

`x_3` = `-pi/6+2*k*pi`

`x_4` = `(7*pi)/6+2*k*pi`

`a_2` = `3/4` = `sin^2 x`

`sinx` = `root()(3)/2`

`x_5` = `pi/3+2*k*pi`

`x_6` = `-pi/3+2*k*pi`

`sinx_4` = `-root()(3)/2`

`x_7` = `(4*pi)/3+2*k*pi`

`x_8` = `(5*pi)/3+2*k*pi`

ahol `k in ZZ`.

Fokokban: 30, 60, 120, 150, 210, 240, 300, 330° + `k*360°`