Answer:
Step-by-step explanation:
First, use the Pythagorean identity that says
[tex]cos^2x+sin^2x=1[/tex] and solve it for cos-squared x:
[tex]cos^2x=1-sin^2x[/tex] so make that replacement into the original equation:
[tex]4(1-sin^2x)=5-4sinx[/tex] and then distribute to get
[tex]4-4sin^2x=5-4sinx[/tex] then get everything on one side so you can factor:
[tex]4sin^2x-4sinx+1=0[/tex]
For the sake of ease, let
[tex]sin^2x=u^2[/tex] so sinx = u. Now we are factoring
[tex]4u^2-4u+1=0[/tex] which factors very nicely to
[tex](u-\frac{1}{2})^2[/tex] Now replace the u with sin(x) and solve for where, on the unit circle, the sin of the angle is equal to 1/2:
[tex]sinx=\frac{1}{2}[/tex] when
[tex]x=\frac{\pi }{6} ,\frac{5\pi}{6}[/tex]
