Trigonometric Formulae? - Tricks:12th Class

    SUPER HEXAGON TECHNIQUE FOR TRIGONOMETRIC FORMULAS

Tricks to remember formulae in Trigonometry

As Trigonometric functions have a lot of applications in different fields,so by using PALM TRICK , the values of  Trigonometric functions for different standard angles can easily be calculated. 

Palm Trick is very easy and useful method to remember all the values for Trigonometric functions.

Now, let us introduce the SUPER HEXAGON FOR TRIGONOMETRIC FORMULAS.

At left side of Hexagon, there is a trigonometric function like sin,tan,sec and their conversions on right hand side of Hexagon, as follows..

1) sin Ө = cos (90-Ө)

2) tan Ө = cot (90-Ө)

3) sec Ө = cosec (90-Ө)

At vertices all important functions.

CLOCKWISE

4) tan Ө = sin Ө/cos Ө

5) sin Ө = cos Ө/cot Ө

6) cos Ө = cot Ө/cosec Ө

7) cot Ө = cosec Ө/sec Ө

8) cosec Ө = sec Ө/tan Ө

9) sec Ө = tan Ө/sin Ө 

ANTICLOCKWISE

10) tan Ө = sec Ө/cosec Ө

11) sin Ө = tan Ө/sec Ө

12) cos Ө = sin Ө/tan Ө 

Observe Direction of Rays

13) tan Ө X cos Ө = sin Ө

14) tan Ө X cosec Ө = sec Ө

15) cos Ө X cosec Ө = cot Ө

16)  sin Ө X cot Ө = cos Ө

Observe the center of hexagon there is "1"

18) sin Ө X cosec Ө = 1

19)  cos Ө  X  sec Ө = 1

20)  tan Ө X cot Ө = 1

Trigonometric Functions and their values- Tricks

Trigonometry

Trigonometry is one of the most important topics in mathematics.

The first type of trigonometric function, which relates an angle to a side ratio, always satisfies the following equation: f(q) = a / b. 

The secondary trigonometric functions are the sine and cosine of an angle. 

The functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (cosec), secant (sec), and cotangent (cot).

Trigonometric functions

The above secondary trigonometric functions are sometimes abbreviated sin(θ) and cos(θ), respectively, 

where θ is the angle, but the parentheses around the angle are often omitted, e.g., sin θ and cos θ.

• The sine of an angle is defined in the context of a right triangle, as the ratio of the length of the side that is opposite to the angle divided by the length of the longest side of the triangle (i.e.the hypotenuse).
• The cosine of an angle is also defined in the context of a right triangle, as the ratio of the length of the side that is adjacent to the angle divided by the length of the longest side of the triangle (i.e.the hypotenuse).
• The tangent (tan) of an angle is the ratio of the sine to the cosine. 

Finally, the reciprocal functions secant (sec), cosecant (cosec), and cotangent (cot) are the reciprocals of the cosine, sine, and tangent.These definitions are sometimes referred to as ratio identities.

Impotance of Trigonometry

• Trigonometric functions relate the angles of a triangle to the lengths of its sides.
• Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications. 
• Trigonometric function is used in oceanography in calculating the height of tides in oceans.
•  The sine and cosine functions are fundamental to the theory of periodic functions, those that describe the sound and light waves.
• Trigonometric function has its applications in satellite systems.

Tricks to remember formulae/values of functions in Trigonometry

PALM TRICK : As Trigonometric functions have a lot of applications in different fields, the values of  Trigonometric functions for different standard angles play an important role. So, considering the applications of Trigonometric functions, the values for Trigonometric functions should be remembered.

Palm Trick is very easy and useful method to remember all the values for Trigonometric functions.

So, let us see the algorithmic procedure to remember the values and its tabular form.

Let us arrange the values for sin and cos 

for sin go on counting right side fingers and for cosine go on counting left side fingers for target angle position.

Let us find Sin 0⁰

        for finding sin value of first angle, count right side fingers of the angle.

     for example here angle is 0⁰

     So, here fingers on right side of zero degree = 0

     The formula is Square root of no of fingers / 2

∴       Sin 0⁰  = √0/2 = 0       and   cos 0⁰    =    √4/2 = 2/2 = 1

      Sin 30⁰  = √1/2 =1/2    and   cos 30⁰ =    √3/2                         

      Sin 45⁰ = √2/2 = 1/√2 and   cos 45⁰ = √2/2 = 1/√2 

      Sin 60⁰ = √3/2            and   cos 60⁰  =    √1/2 = 1/2 

        Sin 90⁰ = √4/2 = 2/2   and   cos 90⁰  =    √0/2 = 0  

                              = 1   
Arrange the above calculated values in tabular form for 0⁰,30⁰,45⁰,60⁰ ,90⁰,180⁰ ,360⁰