Using proportions, it is found that the original angle is of 2250º. The co-terminal angle is of 90º, which has sine equals to 1.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The proportion considered in this problem is that 2pi is equivalent to 360º and we want to find the equivalent angle to 200pi/16, hence the rule of three is given by:
2 pi - 360º
200pi/16 - x º
Applying cross multiplication:
[tex]x = \frac{1}{2\pi} \times 360 \times \frac{200\pi}{16}[/tex]
[tex]x = 2250^\circ[/tex]
The original angle is of 2250º.
To find the co-terminal angle, we find the remainder of the division of 2250 by 360, hence it is of 90º, which has sine equals to 1.
More can be learned about proportions at https://brainly.com/question/24372153
