Trigonometry/Soh-Cah-Toa

The Mnemonic

 * $$Soh-Cah-Toa$$

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

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

=Trigonometric definitions= 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 Link
These links from the Khan Academy are useful for this topic.
 * Basic Trigonometry Soh-Cah-Toa (sin and cosine)
 * Basic Trigonometry II Soh-Cah-Toa (starting with tan)

Exercises: (Draw a diagram!)

 * A right triangle has side a = 3, b = 4, and c = 5.
 * Calculate the following:
 * $$\sin(A),\cos(A),\tan(A)$$


 * A different right triangle has side $$c=6$$ and $$\sin(A)=0.5$$.
 * Calculate side a.