# Setting up sine and cosine functions.

You may have heard the term SOHCAHTOA in your Math or trig class. This is a clever way to remember the trig functions, sine,cosine, and tangent. These functions are applied to right triangles. In order to understand the ratios of sine and cosine we need to identify the sides of the triangle. The hypotenuse is always opposite the right angle, the opposite side is opposite the angle, and the adjacent is next to the angle. Next let's look at the ratios. Sine is opposite over hypotenuse. Cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. If you abbreviate you get SOHCAHTOA. If you are like many folks a short illustration will help, so check out the short video.

For summary of the video go to MooMooMath/Sine

Transcript of Setting up Sine and Cosine
Setting Up Sin/Cosine
Welcome to MooMooMath. Today we are going to set up how to find sin and cosine. Let’s review, the Sine of an acute angle equals opposite over hypotenuse. The cosine of an acute angle equals adjacent over hypotenuse. How do we decide which side is which? First let’s look at angle A from angle a we have to look at our reference sides. If we go to our opposite side that will be our opposite side and I will label this o for opposite. The hypotenuse (labeled h) is always across from the fight angle so the adjacent or next to angle A. (labeled a) Now let’s add some measurements. Let’s say the opposite side is 6 and the hypotenuse is 10 in order to find my sin it will be the opposite over hypotenuse so the Sin of angle A will equal 6/10 which is my opposite over hypotenuse. The cosine is the adjacent over the hypotenuse I don’t know the length of a so I can use the Pythagorean Theorem to find this side. So I will take a squared plus b squared which is 6 plus c which is 10 squared so to write this out I get  64 so (a )must be the length of 8 (take the square root of 64) I can now solve for A The Cos of A will be 8 over 10 because it is adjacent over hypotenuse and that is how I would solve. You can also look from angle B the opposite side would be the lower angle here, the adjacent is here and the hypotenuse is always opposite the right angle. So the opposite and adjacent will flip according to which angle. Hope this was helpful.