There are values of t so sin t =.3 and cos t=-.6

 A pretty straight way to determine this is to evaluate t for both of these equations, although it may not be the method you are looking for.

For sin (t) = .3
arcsin (.3) = t (that is what the arcsin is)
In degrees that is 17.457603124.
Thus sin (17.457603124) = .3

For cos (t) = -.6
arccos (-.6) = 126.86989765

Now there are multiple values of t where cos (t) = -.6. The values repeat every 360 degrees so, the cos of −233.13010235 degrees or 486.86989765 degrees also produce -.6. But none of these match the t given by the first equation. So no, there is no value of t that produces sin(t) = .3 AND cos(t) = -.6.

What's the question in this I don't understand