Sohcahtoa

"Sohcahtoa" is the easy way to remember how Sine, Cosine and Tangent work.

Sohcahtoa

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

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 (and opposite is opposite the angle):

 

Sine, Cosine and Tangent

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

The calculation is simply one side divided by another side ... you just have to know which sides!

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

Sine Function:	sin(θ) = Opposite / Hypotenuse
Cosine Function:	cos(θ) = Adjacent / Hypotenuse
Tangent Function:	tan(θ) = Opposite / Adjacent

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.
  

Example

How do you use it?

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

The classic 30° triangle has a hypotenuse of length 2, an opposite side of length 1 and an adjacent side of √(3):

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!)