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

 

Degree/radian measures

Hello students, in this section we are going to discuss the radian and degree measure from Tamilnadu education board . In mathematics we use some units for measuring the angle. Such as degree, radians and revolution. A degree measures is denoted by this symbol ° and by the deg. it identifies the plane angle, tells the direction of anything and also tells the size of angle. A radian measures is denoted by the superscript ‘ c ‘ and by the rad. Such as 3.4 radian can be represented as 3.4c and 3.4 rad. Radian describes the correlation between the arc length and arc radius. For more on radian visit this.

The formula to covert the degrees to radian â´±^c = â´±° * π / 180 or 1 degree =п / 180 radians

Example 1:- Convert the 70 degree to radian

Solution: – According to the formula 1 degree = n /180 radians

70 degree = 70 * 3.14 / 180

= 219.8 / 180

= 1.22 radians

The answer is 70 degree is equals to 1.22 radians

The formula to covert the radians to degrees â´± = â´±c * 180 / π or 1 radian = 180 / n

Example 2: – Change the 9 radian to degree.

Solution: – According to the formula 1 radian = 180 / п degrees

9 radian = 9 * 180 / 3.14

= 1620 / 3.14

= 515.92 degrees

The answer is 9 radians is equals to 515. 92 degrees

Like following above formulas we can change any radian numbers to degrees and degree to radian numbers. Below are the Some common radians and degrees measures for angles are : –

Angles in deg 30° 45° 60° 90° 180° 360°

Angles in rad π /6 π /4 π /3 π /2 π 2π

In upcoming posts we will discuss about Problems related to Transformations and Learn Parabolic Functions and Axis of Symmetry. Visit our website for information on Binomial Probability Distribution