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In Trigonometry, the **Sin**, **Cos** and **Tan** ratios can be used when trying to
work out the values of sides and angles of a right angle triangle.

The improvised word "**SohCahToa**", is a handy way for remembering how things work.

A right angle triangle has  3 specific sides.

If we were focusing on the other internal angle than the red angle shown in the diagram above.

The __hypotenuse__ side remains the same, the side opposite the right angle.

But the sides which are the __opposite__ and __adjacent__ sides, would switch around.

So for the triangle above, we could also have.

After becoming familiar with the names and locations of the sides.

Next is the point where "**SohCahToa**" comes in.

For a triangle such as the one above, with a specified angle

sin

cos

tan

We can see how this works in practice with some examples.

From the following triangle what are the ratios **sin**, **tan** and **cos** of the
angle **45°**?

sin

cos

tan

Establish the length of side **b** in the following triangle.

Side **b** is the __ADJACENT__ side to the angle **60°**.

We already know the __HYPOTENUSE__ length, so here we can make use of the **cos** ratio,
as this deals with both of those sides.

cos

Sometimes in some situations, you need to draw your own triangle from the information given, to find out further values.

If sin**A** = \bf{\frac{4}{5}} in a right angle triangle.

What are the values of cos**A** and tan**A**?

As sin = \tt{\frac{OPP}{HYP}}.

With the information from sin**A**.

We can draw the right angle triangle with angle **A**, an * opposite* side of
length

The length of the remaining * adjacent* side

Now:

cos

tan

If we consider the following right angle triangle.

sin

From this information, we can obtain another way to write tan

Inverse Trig Functions perform the action of going backwards from the Trig ratios seen earlier in the
page.

They are notated in the form:

sin^{-1}(** x**) , cos

These function have buttons that feature on most standard calculators.

If you have  2 values

sin(

then the inverse is sin

This fact can be used to work out angles in a right angle triangle if certain side lengths are known.

What is the size of the red angle in degrees?

In the above right triangle, we have the lengths of the Adjacent and the Hypotenuse side.

This means that we can use the inverse "cos"
function to establish the size of the angle.

cos(**θ**) = \bf{\frac{7}{10}} => cos^{-1}(\bf{\frac{7}{10}}) = **θ**

With the use of a calculator, making sure it's set to degrees:

cos^{-1}(\bf{\frac{7}{10}}) = **45.57**

The size of the red angle is **45.57°**.

In degrees, what size of angle **θ** gives sin(**θ**)
= **0.6**?

sin

The size of the angle **θ** is **36.87°**.

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