Question

How do I solve these problems without using a calculator?

Answer 1

N 1

Remember that

`\begin{gathered} \cos (60^o)=(1)/(2) \\ \sin (60^o)=\frac{\sqrt[]{3}}{2} \end{gathered}`

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

`\sin (60^o)=\frac{\sqrt[]{3}}{2}`

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