How do I solve these problems without using a calculator?

N 1
Remember that
[tex]\begin{gathered} \cos (60^o)=\frac{1}{2} \\ \sin (60^o)=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]therefore
the angle theta is equal to
180-60=120 degrees
the angle lies in the second quadrant
the answer part 1 is 120 degrees or 2pi/3
N 2
Remember that
[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]and the value of the tangent is positive
that means
the angle theta lies on the I quadrant
the angle theta is equal to 60 degrees or pi/3
N 3
i will assume that u/d is undefined
so
Remember that
the value of the sine is equal to 1 when the angle is 90 degrees (I quadrant) for the given interval [0,360]
therefore
the angle theta is 90 degrees or pi/2