I need help with the following equations to solve between 0 and 360°:
1.
2.
3.
4.
For 1, I've obtained x = 45°, 225°, 315°, 360°.
For 2, I've 30° and 75°.
For 3, hopeless.
For 4, no idea.
sin(2x)=1/2
let b=2x
values of b that give +1/2 are 30 and 150
so sinb=1/2 where b =30,150
b=2x implies 2x=30 and 2x = 150
sin^2 x =1/2 is the same as (sinx)^1/2 =1/2,
thus sinx = sqrt(1/2)
values of x that give +1/sqrt(2) are 45 and 135
cos(x-30)=1
let x-30=b
so cosb=1
values of b that give +1 are 0 and 360
this means x-30=0 and x-30=360
cos^2 x =3/2
this is the same as cosx=sqrt(3/2)
but sqrt(3/2) is > than 1.
cosx has a range of 1>y>-1
so there is no solution