As naught101 says, your particular case here is a sinusoidal wave with a quiet third harmonic. To hear what this sounds like at an audible frequency, go to http://meettechniek.info/additional/additive-synthesis.html in a browser that supports the Web Audio API (like Firefox or Chrome), turn the audio on, and set it like this:
H1 there represents your
(16/15)cos(½ t), although as the default frequency of this online synthesizer is 440, we've effectively scaled it to cos(440 × 2π × t), and (16/15) has just been normalised to '1.000'. H3 represents the
-(1/15)cos(2t) bit, again scaled up in frequency - ideally the volume would be 0.0625, which is 1/16 of the volume of the fundamental (H1), but 0.065 is close enough.
You may not find it sounds that interesting after all! In fact all waveforms that are strictly periodic with no variation tend to sound quite boring (to me at least) - they'll all just be a static hum or buzz. It's usually the variation in the shape of the waveform over time that makes it sound interesting.
Because of the nature of that particular equation it's easy to reproduce its output in an additive synthesizer. In the more general case, one way to hear an equation is to sample its output - generate the 'y' for certain values of 't' (at a certain sample rate such as 44.1 kHz, which would generate 44100 samples per second) - and play back the list of y values as PCM digital audio data.
As an example, one audio editor I use to do this is the (quite old) Adobe Audition 1.5, that can load in a text file, interpret each line as a sample value, and play the resulting waveform back like a WAV or any other audio file. To do this, it wants the y values scaled to fit within the range of 8-bit or 16-bit data (e.g. within −32,768 to 32,767 for 16-bit) and rounded to the nearest integer, so the text file would look like (e.g.)
You could ask on https://softwarerecs.stackexchange.com/ to see if there's any newer / free audio editor that can import textual sample data like this.
If you can do any coding at all, it should be fairly easy to find a library that can write audio files (e.g. the Python language has the 'wave' module) once you have generated a list of sample values, so you can easily write an audio file in a common format from your program.
This kind of sampling is likely to be what Dom's excellent wolframalpha suggestion will be doing internally, though I couldn't get it to work in my browser! To get your equation into the audible range, you could scale it - e.g. using (16/15)cos(250 * 2π * t)-(1/15)cos(1000 × 2π × t) will give you a wave with a fundamental frequency of 250Hz (assuming t is in seconds).
One thing to watch for when sampling is aliasing - to avoid this, you need to sample at a rate of at least double the value of any frequency component of the waveform generated by the function.