Question

What are the trigonometric ratios

Answer 1

The trig ratios are a set of numbers that are properties
of every angle.

When the angle is in a right triangle, they can be defined
like this:

Sine (sin) of the angle:        (opposite leg) divided by (hypotenuse)
Cosine (cos) of the angle:  (adjacent leg) divided by (hypotenuse)

Tangent (tan) of the angle:      (opposite leg) divided by (adjacent leg)
Cotangent (cot) of the angle:  (adjacent leg) divided by (opposite leg)

Secant (sec) of the angle:  (hypotenuse) divided by (adjacent leg)
Cosecant of the angle:       (hypotenuse) divided by (opposite leg).


The size of the right triangle doesn't matter, only the ratios of
pairs of sides.  That will always be the same number for the
same angle, no matter how big or small the triangle is.

There's no easy way to calculate the numbers for an angle. 
You just have to look them up, using tables in books, or online
(try 'cosine 29' on Google), or on most hand-calculators. 

Answer 2

The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring 90 ° ). Remember that the two sides of a right triangle which form the right angle are called the legs, and the third side (opposite the right angle) is called the hypotenuse.