```Question 28417
Well first, sin, cos and tan are cyclical functions...they repeat themselves, so there are in fact an infinite number of answers for answer question. What the question usually tells you is a range of angles to quote from.

Anyway, you haven't, so you might as well quote the one answer that your calculator will store.

sinA = 0.2356
so there is an angle of a right angled triangle such that when you divide the opposite length by the hypotenuse length, that ratio is 0.2356.

Method:
well, we have an equation. And one fundamental rule of equations is "to remove something, you do the opposite".

We have sinA and we want the angle A by itself. So we need to remove the "sin" bit. So, the opposite of sin, as shown on your calculator is sin^(-1).

so A = sin^(-1)(0.2356).
A = 13.627 degrees
--> A = 14 degrees.

Physically, the opposite of sin being "sin^(-1)" doesn't make sense...it is just the way we write "opposite of sin", that is all.

Second one:
tanA = -2.4567
A = tan^(-1)(-2.4567)
A = -67.851 degrees.

Your calculator will convert this to degrees-minutes-seconds, using relevant button: ask your teacher to tell you which it is.

A = -67.851 degrees becomes
A = -67degrees 51minutes and 4seconds

Doing it from "first principles" is as follows:
.851 of 60minutes is 0.851*60 --> 51.06 minutes....so 51minutes

and
0.06 of 60 seconds is 0.06*60 --> 3.6 which is 4 seconds to the nearest second.

jon.
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