Given:
![\sin (310\text{\degree)}](https://img.qammunity.org/2023/formulas/mathematics/college/7hmx6cud9533ab78kfl0cl0c41zilp8hzq.png)
You need to remember that in Trigonometry:
Therefore, knowing that the angle given is:
![310\text{\degree}](https://img.qammunity.org/2023/formulas/mathematics/college/l46hw65xr1my3pda99h8x2ia959bxm80mr.png)
You can identify that it is between 270 degrees and 360 degrees:
![270\text{\degree}<310\text{\degree}<360\text{\degree}](https://img.qammunity.org/2023/formulas/mathematics/college/gixditlql7pwj5bckxmalfao9zumbisvoe.png)
Hence, it must be in Quadrant IV.
Look at the picture below:
Therefore, in this case, you can determine that:
![(x,y)=(\cos (310\degree),\sin (310\text{\degree))}](https://img.qammunity.org/2023/formulas/mathematics/college/lxn0m70byng9bmhhvy8ig4nnh577izh5p1.png)
Hence, the answer is: Option f.