Slightly tangential (hee hee) and by no means meant to hijack the thread, my old maths prof drilled the acronym SOHCAHTOA into us with the following:
Sly old Hitler copped a headache taking over Austria.
As to the question, you can use the cosine function to calculate power factor in electricity. In fact the power factor IS the cosine of the angle between the adjacent and hypotenuse of a ‘power triangle’.
If I want to find out how much sunlight is going to come in through the window of the house I am designing, I need to use trig (plus the time, date, and the location and orientation of the house and its windows) to find out what angle the sunlight will be making with the window during each season. Once I know this, I can figure out how much sunlight is entering, and then how much energy will be stored in the house’s massive walls each day. Then I can calculate how thick the house’s insulation needs to be to lose heat more slowly than it arrives.
Result: a house that needs no bulk heating or cooling, saving the owner thousands. (The house may still need ventilation, humidification or dehumidification, but those can be handled with air-to-air heat-exchangers. Or by opening the window.
Navigation. Take bearings on two landmarks on shore, a known distance and direction from each other. A few minutes with a pencil and some tables, and the sine and cosine rules, and you’ve solved the triangle, giving your distance away from the landmarks. (Or you can just cheat and plot your position on the chart. 
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I can’t say for sure unless I see the same movie but the tech is probably a sonar technician and he’s talking about a sound coming in. I don’t know what they see on a screen, I had the impression that much of sonar analysis was done by ear (IANANT). That being said, I can’t imagine when a “classic sine wave” would ever be heard on sonar. Engine sounds and other underwater sound detected by passive, or reflections from active sonar (when they ping), would be more complex and noisy than a sine wave, which is heard as a pure tone at a single frequency, so pure that it gets annoying if it continues for long.