Let's check the given function:
![\sin \theta=\frac{\sqrt[]{3}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/xlbqkc4ononzdmzcay8b9sgbke7osana1w.png)
Where sinθ is positive in quadrants 1 and 2.
Also, sinθ= opposite side/ hypotenuse:
Then:
Now, the first angle can be found solving theta:
![\theta=\arcsin (\frac{\sqrt[]{3}}{2})](https://img.qammunity.org/2023/formulas/mathematics/college/yxvro50y1su5xrusv3xurpmono2bw0fcxv.png)

To find the second angle we use:

Then:


Now, sinθ will be again positive when we complete a whole circle.
Then, we use
If a circle has 2π, then 2π+1/2π =5/2π is when sinθ is positive again.
There, we use:
120* 4= 480
Then:
![\sin (480)=\frac{\sqrt[]{3}}{2}](https://img.qammunity.org/2023/formulas/mathematics/college/ii5e010bpkh14utxwgenyl7v06akh7s5n6.png)
Hence:
