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# Sin, Cos, Tan

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## 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.

**Here are the three equations you need to know:**

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 30^{0} then the **Sine** ratio (Opposite divided by Hypotenuse) will always be 0.5

**Therefore, sin** 30^{0} = 0.5

**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:

**S**weaty **O**ld **H**orses **C**hase **A**fter **H**ens **T**hat **O**ffer **A**dvice.

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**.

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:**