Do you find it difficult to remember what to divide by what to give which trig ratio? Follow these simple memory aids so that you never forget how to find sine, cosine and tangent again.
These days most schools and institutions provide their students with formula sheets for tests and examinations as well as in normal class time; however, your mathematical life will still go much more smoothly if you "just know" how to obtain the sine, cosine and tangent of an angle.
Basics: the Three Sides of the Triangle
Before you go on, make sure you can label the three sides of a right-angled triangle:
- hypotenuse
- adjacent and
- opposite.
Review how to do this here.
SINE
To find the sine of an angle, divide the length of the opposite side by that of the hypotenuse.
SIN θ = OPPOSITE ÷ HYPOTENUSE
See a worked example of finding sine θ.
COSINE
To find the cosine of an angle, divide the adjacent side by the hypotenuse.
COS θ = ADJACENT ÷ HYPOTENUSE
See a worked example of finding cos θ.
TANGENT
To find the tangent of an angle, divide the opposite side by the adjacent.
TAN θ = OPPOSITE ÷ ADJACENT
See a worked example of finding tan θ.
Mnemonics
If you take the initial letter of each word, each ratio calculation can be represented by three letters:
- SOH for sine
- CAH for cosine and
- TOA for tangent.
A lot of people simply learn these as if they were (perhaps Japanese-sounding) words: SOH - CAH - TOA ("so - ka - towa").
Another method is to make up sentences in which the words begin with these letters in order, such as:
- Send Out Hats, Caps And Helmets To Our Army
- Six Overseas Holidays Calmed Anne's Hyperactive Toddler Over August
- Sad Or Hungry? Cookies Are Hot, Tasty, Orange and Amusing
Triangles
Each of the three formulae can be drawn in a triangle. Memorizing these now will also help later when we use them for solving trigonometric equations. View these here.