How to solve sin cos tan - SOHCAHTOA

HOW TO SOLVE CONTENT
SIN COS AND
TAN - This document explains how to find Sin, Cos,and Tan
SOHCAHTOA of a right triangle given either all side lengths or angle
and one side length
[Document subtitle]
P Denise Smith Of TutorByDenise
404-939-3806

www.tutorbydenise.com

HOW TO SOLVE SIN COS AND TAN - SOHCAHTOA

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

OK, let's see what this is all about.
Firstly, 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

P DENISE SMITH OF TUTORBYDENISE 404-939-3806 1

HOW TO SOLVE SIN COS AND TAN - SOHCAHTOA
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 ... we 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!)

P DENISE SMITH OF TUTORBYDENISE 404-939-3806 2

HOW TO SOLVE SIN COS AND TAN - SOHCAHTOA

How to Remember

Well, "sohcahtoa" may be easy for you to remember ... but here’s another way to help it:
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.

P DENISE SMITH OF TUTORBYDENISE 404-939-3806 3