The study of trigonometry begins with the right triangle. The three main trig functions (sine, cosine, and tangent) and their reciprocals (cosecant, secant, and cotangent) all tell you something about the lengths of the sides of a right triangle that contains a given acute angle
— like angle x in the figure below.
The longest side of this right triangle (or any right triangle), the diagonal side, is called the hypotenuse.
The side that’s 3 units long is referred to as the opposite side because it’s on the opposite side of the triangle from angle x, and the side of length 4 is called the adjacent side because it’s adjacent to, or touching, angle x.
SohCahToa is a meaningless mnemonic that helps you remember the definitions of the sine, cosine, and tangent functions. SohCahToa uses the initial letters of sine, cosine, and tangent, and the initial letters of hypotenuse, opposite, and adjacent, to help you remember the following definitions. (To remember how to spell SohCahToa , note its pronunciation and the fact that it contains three groups of three letters each.)
For the triangle in the preceding figure:

The other three trig functions are reciprocals of these: Cosecant (csc) is the reciprocal of sine, secant (sec) is the reciprocal of cosine, and cotangent (cot) is the reciprocal of tangent.
For the triangle in the preceding figure:
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):
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 ... you 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...
s in(
θ
) = o pposite / h ypotenuse
Cosine Function: ...cah...
c os(
θ
) = a djacent / h ypotenuse
Tangent Function: ...toa
t an(
θ
) = o pposite / a djacent
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
Cosine
Tangent soh...
...cah...
...toa
sin(30°) = 1 / 2 = 0.5 cos(30°) = 1.732 / 2 = 0.866 tan(30°) = 1 / 1.732 = 0.577
(get your calculator out and check them!)
Well, "sohcahtoa" may be easy for you to remember ... but here’s another way to help you remember:
S ailors O ften H ave C urly A uburn H air T ill O ld A ge.
Or perhaps you prefer one of these:



S ome O ld H orses C an A lways H ear T heir O wners A pproach.
S ome O ld H en C aught A nother H en T aking O ne A way.
S ome O ld H ippie C aught A nother H ippie T ripping on A pple
A way of remembering how to compute the sine , cosine , and tangent of an angle .
SOH stands for Sine equals Opposite over Hypotenuse .
CAH stands for Cosine equals Adjacent over Hypotenuse .
TOA stands for Tangent equals Opposite over Adjacent .

Example:
Find the values of sin θ, cos θ, and tan θ in the right triangle shown.
Answer: sin θ = 3/5 = 0.6 cosθ = 4/5 = 0.8 tanθ = 3/4 = 0.75
This triangle is oriented differently than the one shown in the SOHCAHTOA diagram, so make sure you know which sides are the opposite, adjacent, and hypotenuse.