Sin, Cos, Tan

Sin, Cos, Tan

The full names for these three ratios are Sine, Cosine and Tangent.

Important: They must always be with an angle, they cannot survive on their own! This was described in the previous section.

Three equations

Here are the three equations you need to know:

What do they mean?

Well, basically they mean that for a particular angle the sides will always be related to each other in the same way (they will be in the same ratio).

Change the angle and obviously the ratios change!

For instance, if the angle is 300 then the Sine ratio (Opposite divided by Hypotenuse) will always be 0.5

Therefore, sin 300 = 0.5

Is there an easy way to learn them?

In a word - no, but here's a few suggestions...

1. Some people just learn them by the initial letters SOHCAHTOA (soh-cah-toa) So, Sine is Opposite over Hypotenuse, Cos is Adjacent over Hypotenuse and Tan is Opposite over Adjacent.

2. You could try a mnemonic (a phrase made up by using the first letter of each word. Here's one we've made up:

Sweaty Old Horses Chase After Hens That Offer Advice.

OK, that was shocking. You can probably make up a much better one of your own! Once you think you have got it in your head, try the test below.

Drag the labels on the triangle into the formula and mark your answer:

3. Formula Triangles - these have the added advantage of giving you the different arrangements of the formulas you need! You may have used them before in Physics. All you do is cover what you want to calculate and what's left is the formula to calculate it. The diagram below shows how this works.

Here's a worked example showing how to find a side. Again, we've called the side we want to find x.

What if you want to find the angle?

This is a bit more difficult! You need to use the inverses of sin,cos and tan. These can be usually be found above sin, cos and tan onyour calculator and are sin-1, cos-1 and tan-1.

Here's another worked example. The angle we want to find is x: