how do I know whether to use degrees or radian?

Some general tips I usually try to think of are:

* If the value in question is more than 6, for example cos(15), you're more than likely in degrees.
* If the value has π anywhere in it - cos(π/6), cos(π/2), etc. - you're in radians.

Generally, radians is the default the higher up in math you go, and I would recommend trying to think in them by default unless told otherwise.  If you could give us the specific question, we might be able to help you see if there was maybe a context clue you missed.

Lastly, as this is an exam question - in an actual exam, I think there would be no harm in asking the proctor which one to use.
Anything using degrees should explicitly say so, either in text or with the degree sign “º”.

Radians are unitless, and do not get any specific marking. At least for pure math, they are the “default” way to measure angles.
You mean how to know if the problem is about degrees or radians if you don't know what you're doing and you can't tell whether an answer is reasonable or not? Well one useful rule of thumb is you're dealing with degrees if the problem has the degree symbol ° in it but radians if you see pi π.

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