If you have a cheap multimeter and it reads 115v then it is fairly sinusoidal. If you have access to a true rms meter and it reads 115v on that and the cheap average reading meter (scaled rms) then it will be sine. If there is a significant discrepancy between the cheap meter and a true rms then it will be modified square( modified sine if you must call it that),
The trick with the modified square inverters to make them work on most loads is to make the peak and the rms values near that of a sine inverter, if you use a square wave of 160v peak then it will run things like radios as the dc supplied to the radio circuit will be the same as peak rectified sine wave. Now this would burn out an incandescent light bulb as the rms would be 160v, but if you restrict the square wave to pulses of half width by delaying the start and finishing early, the rms value comes to about 115v.
If you measure ac with a true rms meter then it will be near 115v , if you rectify and measure peak it will be about 160v as for a true sine, but if you use a cheap ac multimeter on the ac range it will be way off ( probably nearer 90v).
The cheap ac meter will measure average, but be scaled to give the equivalent rms voltage on a true sine wave and on any other waveform it will be way out.
Another test is to feed the inverter via a low voltage transformer (say 2v) to a reasonable bass loudspeaker, use a pot if necessary to avoid overloading the speaker. The difference between a true sine and a modified sine will be very obvious.
The snag here is that many cheap sine inverters are not filtered desperately well and you will also hear higher frequency ripple so just listen to the 60hz bass note. The modified wave inverter will sound as though the speaker is grossly over loaded no matter how much you reduce the input.
In the end there is still the element of gamble unless it is a true sine inverter with about 3 times the capability of starting the fridge motor. Many modified square inverters will run fridges ok as long as they have enough reserve to start them, although the motor may run a bit hotter. A true sine inverter will run it properly but unless it is way over size it may still fail to start it.
My experience is that washing machines ( speed controlled dc motor ones )and laptop power supplies are the ones that come to grief on modified wave inverters.
The other devices that won't work are drills and grinders and jigsaws fitted with a variable speed drive, if you have one of these and it runs then you can be fairly sure you have a sine inverter.
Flux