Definition of the Trigonometric Functions of an Acute Angle

Before going to discuss the definition of the Trigonometric Functions of an Acute Angle let's know about acute angle. An acute angle is an angle which is always lesser than 90 degrees. It does not include 90 degrees anyways. In order to find Trigonometry functions we need an acute angled triangle. And the triangle must be a Right Triangle. The angle which is of 90 degrees is called the Right Angle in a triangle. The opposite side to a right angle is called hypotenuse and rest sides will be called as legs of that triangle.

 
Here three legs are associated with the angle θ. One is the hypotenuse which is belonging to the angle θ. The second is opposite side and the last is the adjacent side. We denote hypotenuse by r, opposite by b and adjacent side by a.
 
In a right angle triangle any two sides of right triangle have a Ratio in the form of a relation which is one to one. It helps to form the different Trigonometry formulas and from this we can derive six formulas as the ratio of hypotenuse and opposite, opposite and adjacent, adjacent and hypotenuse and so on.
Now let see the trigonometry function of acute angles θ in the form of ratio of the sides of a right triangle are:
1: sinθ= b/r
2: cosθ= a/r
3: tanθ= b/a
4: cscθ= r/b
5: secθ= r/a
6: cotθ= a/b
Note that sinθ is reciprocal of csc θ, cos θ of sec θ and tan θ of cot θ.
Now see the Pythagorean formula for r, ‘a’ and ‘b’.
Here hypotenuse is always equal to the Square root of the addition of square of opposite side and adjacent side in any right triangle.
r² = a² + b²               
Just like this opposite and adjacent also can be find by this formula:
   a² = r² - b²            
And
    b²= r² - a²           
These are some Trigonometric Functions of acute angles.