# What are the 6 basic trigonometric functions?

Jan 31, 2015

These are all derived from the ratio's in a (right-angled) triangle.

If we divide the length of a side by the length of another side, we have a trigonometric function.

Lets take $\angle A$. Then there are six possible combinations for this division ($h$, $a$ and $b$ are the sides)

sine : $\sin A = a / h$
cosine : $\cos A = b / h$
tangent : $\tan A = a / b$

These three are called the basic functions.
You will find them on most calculators.

Note that: $\sin \frac{A}{\cos} A = \frac{a / h}{b / h} = \frac{a}{b} = \tan A$

The other three are:
cosecant : $\csc A = h / a = \frac{1}{\sin} A$

secant : $\sec A = h / b = \frac{1}{\cos} A$

cotangent : $c t g A = b / a = \frac{1}{\tan} A$

Normally these are not on a calculator, as they are easy to get from the other three.

(picture from Wikipedia) **