有關三角學既問題，求助?

1.How many roots are there in the equation Sin2x=0.5 where 0°＜x＜360°?
Sol
0°＜x＜360°
0°＜2x＜720°
Sin(2x)=0.5
2x=30° or 150°or 390° or 510°
x=15° or 75°or 195° or 255°
4 roots

2.Find the values of θ from 0° to 360° inclusive satisfying the equation
5Sin^2 θ－2Sin θCos θ－3Cos^2 θ=0
Sol
5Sin^2 θ－2Sin θCos θ－3Cos^2 θ=0
(5Sinθ+3Cosθ)(Sinθ－Cosθ)=0
(1) 5Sinθ+3Cosθ=0
5Tanθ+3=0
Tanθ=－3/5
θ=180°－ArcTan(3/5) or θ=360°－ArcTan(3/5)…………………..
(2) Sinθ－Cosθ=0
Tanθ=1
θ=45° o θ=135…………………………………………………………..

1)
sin(2x)=0.5
2x=30 or 2x=150
x=15° or x=75°
There are two roofs

2)
5sin² θ－2sin θ cos θ－3cos ² θ＝0
sinθ=-cosθ or sinθ=(3 cosθ)/5
tanθ=-1 or tanθ=3/5
θ=180-45 or θ=360-45 or θ=30.96375653 or θ=180+30.96375653
θ=135 or θ=315 or θ=30.96375653 or θ=210.9637565