# What is Sine, Cosine and Tangent?

The Sine, Cosine and Tangent functions express the ratios of sides of a right triangle.

You can remember this by the acryonym SOHCAHTOA:

- SOH: ##sin = “opposite”/”hypothenuse”##
- CAH: ##cos = “adjacent”/”hypothenuse”##
- TOA: ##tan = “opposite”/”adjacent”##

Remember that these are not properties of a triangle, but of an angle.

This triangle for example:

If we take the ##sin(30°)##, it is equal to ##”opposite”/”hypothenuse” = 1/2## The ##sin(60°)## however is not equal. It is ##”opposite”/”hypothenuse” = sqrt(3)/2##

So, the trigonometric functions are not properties of triangles, but of angles.

**Why is this useful?**

There are so many uses for the trig functions, but one of the easiest is to solve a triangle.

For example: what if I asked you what the length of the line |BC|

There are two things we know of this triangle. The angle ##|Â| = 40°## and the side ##|AC| = 6##. To find |BC|, we need to find a function that relates ##|AC|,|Â|## and ##|BC|##. The answer is ##tan(40°) = “opposite”/”adjacent” = |BC|/|AC| = |BC|/6##

So to find |BC|, we solve for |BC| in the last equation: ##tan(40°) = |BC|/6## ##tan(40°) * 6 = |BC|##

But now we face a problem: we don’t know the value of ##tan(40°)##. For this, there exists a simple device, called a calculator. Smply enter ##tan(40°)## in your calculator. I like to use Google where you should enter ##tan(40 ” deg”)##. This gives you ##0.839099631##.

=> ##|BC| = 6*0.839099631 = 5.03459779##

Now, as a challenge for you: find ##|AB|## (hypothenuse)

Hope this helped.

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