When giving an angle measure in radians, should we explicitly state that it's in radians?

Question

Let's say you are solving the equation $\arcsin(1) = x$ in radians. Would you write the answer as $\frac {\pi}2$ radians or just $\frac {\pi}2$? I see both methods being used, and I am aware that radians are a dimensionless quantity. However, it seems odd to just say, "The angle is $2$" rather than "The angle is $2$ radians."

Answer 1

People write $\arcsin1=\frac{\pi}{2}$, if only because any alternative approach would be unwieldy in more complicated expressions, such as if you evaluate $\int_0^x\arcsin tdt$ with integration by parts. But if you need to specify an angle in radians without it seeming like it's no angle at all, you could say $\frac{\pi}{2}\operatorname{rad}$. (You'll find other symbols here.)

Answer 2

Yes, if you are describing some property of a geometrical object, like angle, it is more common to say the units in what angle is actually measured.

But when you solve an equation like $$\arcsin(1)=x$$ you can just write $x=\frac{\pi}{2}$ since, firstly, everybody understand that it is not $\frac{\pi}{2}$ degrees(which is weird). And secondly, nobody uses degrees solving equations.