Trig question

Question

My math is online and the helper says that sin∅= y/r= (5√74)/74 = 144.5° . how do u convert that fraction into degrees. 

I did try the inverse of ∅=sin^-1(y/r) , but for my example that only comes out to 35.53767779

Answer 1

sinθ is a number, not an angle.  The angle is θ.

 

If sinθ = 5√74/74 then θ lies in quadrant 1 or 2.

 

If θ lies in quadrant 1,and θ lies between 0° and 360°,                   then θ = sin^-1(5√74/74) ≈ 35.5°

 

If θ lies in quadrant 2, then θ ≈ 180° - 35.5° = 144.5° 

 

                                                                       

Answer 2

Take the inverse of the trig function.

 

θ = sin^-1(y/r)

 

 

where   y/r   is your fraction.