@professionalbronco That's really great that you're thinking about triangles!
Here's the thing-- think about what \(x\) is. It's the angle that we're looking at when trying to find the ratios.
What \(\text{sin}(30^{\circ})=\frac12\) says is that the ratio of the side opposite of a \(30^{\circ}\) angle in a triangle TO the hypotenuse is always equal to \(\frac12\).
So, if you are looking at the graph of \(y=\text{sin}(x)\), plugging in \(x=30^{\circ}\) gives you \(y=\frac12\). This means that \((30,\frac12)\) will be on the graph.
Basically, whatever you plug into \(x\), that's the angle we're looking at. If you plug in \(x=15^{\circ}\), we're now looking at a \(15^{\circ}\) angle in a right triangle.
Wait-- let's go back to the point \((30,\frac12)\). Try doing \(\text{sin}(30)\) on your calculator. If you get \(\frac12\), great! But you actually might get something really weird (like -0.988).
If you do get something weird, this goes back to what the lesson was talking about, degrees vs. radians! Use what you learned in the lesson to figure out what \(30^{\circ}\) is in radians. Then, try to take the sine of that value. That should give you \(\frac12\).
Here's a tip to remember-- ALWAYS make sure whether you're using degrees or radians. If you're using degrees, set your calculator to degrees. Same thing with radians.
One last note: you shouldve gotten that \(30^{\circ}\) is equal to \(\frac{\pi}{6}\) radians. So, does that mean we should graph \((30,\frac12)\) or \((\frac{\pi}{6},\frac12)?\)
Well, it depends on the graph. If the graph tells you to graph the points in degrees, use 30. If it says radians, use \(\frac{\pi}{6}\).
But, just try to think about graphing both points. \(30\) is pretty huge when we're graphing right? Especially compared to how small \(\frac{1}{2}\) is. Radians, on the other hand, are much smaller. It's so much easier to find \(\frac{\pi}{6}\) because it's smaller. So, graphs often use radians by default.
