Need Help with Trig?

Question

I have a few trig questions I'm just not sure and/or don't understand.

1) tan θ =.5890 in Q1
2) 390°= ?? what in rad.
b) reference angle = ??what in deg.
c) reference angle= ?? what in rad.
3) 4 cos (-π/4)
4)sin 3x if x=π/6

I have these answered but I'm not sure if I have them right. PLEASE HELP!! thanks.

Answer 1

1)tan θ =.5890 ----> θ=30.498 deg.

2) 390° =?? in rad.
rule Ar/π =Ad/180 (where Ar is the angle in rad. & Ad is the angle in deg.)
so Ar=π*390/180=3.14159 * 390/180=6.806784

b) 390°---->390-360=30° (subtract 360 until the number between 0-360)
c)30°===>π*30/180=0.523599 in rad

3) 4 cos(-π/4)
as a fact π----> 180° so π/4---->45°
cos(x)=cos(-x)
so 4cos(-π/4)= 4cos(-45°)= 4cos(45°)= 4sqr(2)/2= 2sqr(2)
=2.82842712

4sin 3x if x=π/6
sin(3π/6)= sin(π/2)=sin90°=1

Answer 2

t=0.5323 rad
2) 390/x=360/2pi so x= 390/360 * 2p=2.1667 pi
b)360 degrees and 2pi rad
4cos(-pi/4)= 4 cos pi/4 = 2*sqrt(2)
sin 3x = sin pi/2= 1