Basic trigonometric functions

In mathematics there is a branch of it that is known as trigonometry which defines relation between the angles and sides of the triangle. In the trigonometry there are some functions that are called as the Basic trigonometric functions and the functions are helpful in defining the relation between the different sides and angles of the triangle. You can also take help of trigonometry calculator available online. You can also try How to do trigonometry step by step. These are denoted as:

If there is a right angled triangle then according to the trigonometric functions we can define the relation as:

1.       Perpendicular / hypotenuse = sin Θ (where Θ is an angle (right angle)),

2.       Base / hypotenuse = cos Θ,

3.       Perpendicular / Base = tan Θ.

There are some formulas of trigonometry that are as follows (more formulas here):

(a) cos 2 (Θ) + sin 2 (Θ) = 1,

(b) 1 + tan 2 (Θ) = sec 2 (Θ),

(c) cot 2 (Θ) + 1 = cosec 2 (Θ),

(d) sin (a + – b) = sin (a) cos (b) + – cos (a) sin (b),

(e) cos (a + – b) = cos (a) cos (b) – + sin (a) sin (b),

If in the given formula a = b then

(f) sin (2 a) = 2 sin (a) cos (a),

(g) cos (2 a) = cos 2 (a) – sin 2 (a),

= 2 cos 2 (a) = 1 – 2 sin 2 (a),

(h) tan (2 a) = 2 tan (a) / 1 – tan 2 (a) .

We will define some other functions as:

(i) sin ² (a) = 1 – cos (2 a) / 2,

(j) cos ² (a) = 1 + cos (2 a) / 2,

(k) tan ² (a) = 1 – cos (2 a) / 1 + cos (2 a) .

In upcoming posts we will discuss about symmetry and Congruent Triangles in Grade XI. Visit our website for information on karnataka state board syllabus