When it comes to trig ratios, in previous math courses we’ve used “SOH CAH TOA” to understand how to orient the different values within the ratios.

meaning:

SOH – Sin = opposite over hypotenuse

CAH – Cos = adjacent over hypotenuse

TOA – Tan = opposite over adjacent

However, we’ve now moved on to using terms that work much more smoothly with graphing. Now, instead of “SOH CAH TOA”, we now have:

Sin = y/r

Cos = x/r

Tan = y/x

In the short term, memorizing a new set of ratios might feel a bit rough, especially since we already have “SOH CAH TOA” memorized, but swapping to these new ratios will be crucial for our learning. It’s also important to note that these “new” ratios are actually exactly the same as the ones we’ve been using before. In this setup…

x = Adjacent

y = Opposite

r = Hypotenuse

The best way to understand this is just by viewing every one of our triangles like they’re on a graph (because they are). While at first, this concept might take a bit of time getting used to, once you’ve got it down, everything will go smoother.