in order to find the value of a trig function by hand, you would need to expand a Taylor series. No way thats happening on a timed exam with any accuracy.

you either have a slide rule, the tables or remember a bunch of values.

and you convert degrees to radians, when needed.

so use the chart to get the values for sin of some angle. In this case 16* is your closest approximation on a timed exam with multiple choice.