Trigonometry/Soh-Cah-Toa

< Trigonometry

The MnemonicEdit


Soh-Cah-Toa



\displaystyle{
\begin{array}{ccc}
\sin(A)&=&\displaystyle\frac{\text{opposite side}}{\rm hypotenuse}\\
\\
\cos(A)&=&\displaystyle\frac{\text{adjacent side}}{\rm hypotenuse}\\
\\
\tan(A)&=&\displaystyle\frac{\text{opposite side}}{\text{adjacent side}}
\end{array}
}

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

Contents

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:

\sin(A)=\frac{a}{c} or opposite side over hypotenuse
\cos(A)=\frac{b}{c} or adjacent side over hypotenuse
\tan(A)=\frac{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:
\sin(A),\cos(A),\tan(A)
Exercise: Find a side
  • A different right triangle has side c=6 and \sin(A)=0.5 .
  • Calculate side a.