Name: Introduction to the Trig Ratios and SOH CAH TOA | Videos | Gan Jing World
Uploaded: 2023-12-01T23:27:30.478Z
Duration: 4 min 17 s
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MooMooMath and Science

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Introduction to Trig Ratios and SOH CAH TOA

Transcript
So these are the trig ratios you will need to memorize
Sin is opposite over hypotenuse
Cosine is Adjacent over Hypotenuse, and Tangent which is Opposite over Adjacent
Some teach it as SOH CAH TOA
Let me explain where that comes from.
SOH COA TOA is SOH is opposite over hypotenuse
COA is Cosine over adjacent, and tangent is opposite over adjacent
You memorize the trig function with SOH COA TOA with the trig ratios. It doesn't matter.
So when do we use these ratios?
We use these three functions. When you don't have special right triangles. When you don't have 30-60 90'3 or 45 45 90 and don't have these special triangles you use these trig functions.
Let's say our reference angle is here so we will say angle c is our Theta or our reference angle. From angle C the opposite angle is AB and the side opposite the right triangle is the hypotenuse and the angle next to C is adjacent because it is next to C So from angle C the side AB is opposite and BC is adjacent, and AC is the hypotenuse. Now let's look at how you use these to solve. 
So I will draw the problem you have here. We have a right triangle and notice our reference angle is 52 degrees. It is not a special right triangle, so this is why we will use trig with this one. We have the steps. First find the reference angle, then label our opposite,adjacent, and hypotenuse from the reference angle.
Then decide which trig function we have.
So the first part I'm just going to show you how to do steps 1-4. Then we will go through how to solve. Then we will go through how to solve them.
We want to use 52 as the reference angle. So from this 52 this side is the opposite and this side is the hypotenuse.,and this is my adjacent. Which two sides am I using?
We will not use hypotenuse. So we will use the adjacent and hypotenuse side. Go back and look at your reference and which trig ratio should you use? I will jot hem down. Opposite hypotenuse,adjacent hypotenuse, opposite adjacent. Which one uses opposite side over adjacent side? That will be our tangent. So that is how we decide which trig function to use. So lets set up tangent of theta which is our reference angle so Tangent of 52 is opposite over adjacent so we will write a ratio x and adjacent is 12 and that is how we set it up.

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