Sohcahtoa
Sohca...what? Just an easy way to remember how Sine, Cosine and Tangent work:
Soh... |
Sine = Opposite / Hypotenuse |
...cah... |
Cosine = Adjacent / Hypotenuse |
...toa |
Tangent = Opposite / Adjacent |
Right Triangle
The names Opposite, Adjacent and Hypotenuse come from the right triangle:
- "Opposite" is opposite to the angle θ
- "Adjacent" is adjacent (next to) to the angle θ
- "Hypotenuse" is the long one
Adjacent is always next to 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 ... you 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:
Sine Function: |
soh... |
sin(θ) = opposite / hypotenuse |
Cosine Function: |
...cah... |
cos(θ) = adjacent / hypotenuse |
Tangent Function: |
...toa |
tan(θ) = opposite / adjacent |
Example: what are the sine, cosine and tangent of 30° ?
The classic 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:
Now we know the lengths, we can calculate the functions:
Sine |
soh... | sin(30°) = 1 / 2 = 0.5 |
Cosine |
...cah... | cos(30°) = 1.732 / 2 = 0.866 |
Tangent |
...toa | tan(30°) = 1 / 1.732 = 0.577 |
(get your calculator out and check them!)
How to Remember
Well, "sohcahtoa" may be easy for you to remember ... but here’s another way to help you remember:
Sailors Often Have Curly Auburn Hair Till Old Age.
Or perhaps you prefer one of these:
- Some Old Horses Can Always Hear Their Owners Approach.
- Some Old Hen Caught Another Hen Taking One Away.