Sohca...what? Just an easy way to remember how Sine, Cosine and Tangent work:

Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent

Right Triangle

OK, let's see what this is all about.

Firstly, the names Opposite, Adjacent and Hypotenuse come from the right triangle:

triangle showing Opposite, Adjacent and Hypotenuse

  • "Opposite" is opposite to the angle θ
  • "Adjacent" is adjacent (next to) to the angle θ
  • "Hypotenuse" is the long one

examples of Opposite, Adjacent and Hypotenuse

Adjacent is always next to the angle

And Opposite is opposite the angle

Sine, Cosine and Tangent

And Sine, Cosine and Tangent are the three main functions in trigonometry.

They are often shortened to sin, cos and tan.

The calculation is simply one side of a right angled triangle divided by another side ... we just have to know which sides, and that is where "sohcahtoa" helps.

For a triangle with an angle θ , the functions are calculated this way:

sin(θ) = opposite / hypotenuse
cos(θ) = adjacent / hypotenuse
tan(θ) = opposite / adjacent


Example: what are the sine, cosine and tangent of 30° ?

A 30° triangle has a hypotenuse (the long side) of length 2, an opposite side of length 1 and an adjacent side of √3, like this:

30° triangle

Now we know the lengths, we can calculate the functions:

sin(30°) = 12 = 0.5
cos(30°) = 1.732...2 = 0.866...
tan(30°) = 11.732... = 0.577...

(get your calculator out and check them!)

How to Remember

I find "sohcahtoa" easy to remember ... but here are other ways if you like:

Practice Here:


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