Trigonometry/Soh-Cah-Toa

The MnemonicEdit


Soh-Cah-Toa\,


\sin A = \frac{opposite\,side}{hypotenuse}\,

\cos A = \frac{adjacent\,side}{hypotenuse}\,

\tan A = \frac{opposite\,side}{adjacent\,side}\,

Soh-Cah-Toa is a mnemonic for remembering how to use sines cosines and tangents to compute lengths in right angle triangles.

Trigonometric definitionsEdit

right triangle

This triangle has sides a and b. The angle between them, C, is a right angle. The third side, c, is the hypotenuse. Side a is opposite angle A, and side b is adjacent to angle A.

Applying the definitions of the functions, we have:

\displaystyle\sin(A) = a / c or opposite side over hypotenuse
\displaystyle\cos(A) = b / c or adjacent side over hypotenuse
\displaystyle\tan(A) = a / b or opposite side over adjacent side

This can be memorized using the mnemonic 'SOH-CAH-TOA' (sin = opposite over hypothenuse, cosine = adjacent over hypotenuse, tangent = opposite over adjacent).

Video LinkEdit

These links from the Khan Academy are useful for this topic.


Exercises: (Draw a diagram!)Edit

Exercise: Find sin cos and tan
  • A right triangle has side a = 3, b = 4, and c = 5.
  • Calculate the following:
\displaystyle \sin(A), \cos(A), \tan(A)
Exercise: Find a side
  • A different right triangle has side \displaystyle c = 6 and \displaystyle\sin(A) = 0.5 .
  • Calculate side a.


Last modified on 6 January 2011, at 12:45