TRIGONOMETRY FOR CLASS 10TH

TRIGONOMETRY BASIC FUNCTIONS 

The word 'trigonometry' is derived from greek words 'tri' means 'three' , 'gon' means 'sides' and 'metron' means 'measures'. It studies the relationship between the sides and angles of a triangle.🔺🔺

The trigonometry ratios are:

1. SINE (sin)                                                                     Perpendicular/Hypotenuse
2. COSINE(cos)                                                                     Base/Hypotenuse
3. TANGENT(tan)                                                               Perpendicular/Base
4. COTANGENT(cot)                                                          Base/Perpendicular
5. SECANT(sec)                                                                   Hypotenuse/Base 
6. COSECANT(cosec)                                                      Hypotenuse/Perpendicular

• Some ratios of sides of a right triangle respect to its acute angles called Trigonometry ratios of the angle. Trigonometric ratios are Sine, Cosine, Tangent, Cotangent, Secant and Cosecant. The standard angles for these trigonometric ratios are 0 °, 30°, 45°, 60° and 90°. These angles can also be represented in the form of radians such as 0, π/6, π/4, π/3, and π/2. These angles are most commonly and frequently used in trigonometry.
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• The values of the trigonometric ratios of an angle do not vary with the lenghts of the sides of the triangle, if the angle remains the same.
  

                                           ANGLES OF TRIGONOMETRY RATIOS

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  We can be say that an equation involving trigonometric ratios of an angle is called a trigonometry identity.

  • SIN A = 1/COSEC A
  • COS A = 1/SEC A
  • TAN A = 1/COT A    OR     SIN A / COS A 
  • COT A = 1/TAN A    OR     COS A / SIN A
  • SEC A = 1/COS A 
  • COSEC A = 1/SIN A 
  • COS² + SIN² = 1
  • SEC²- TAN² = 1  OR  1+ TAN² = SEC²  
  • 1+COT² = COSEC^{2  OR}  COSEC²-COT² =1

• TRIGONOMETRY RATIOS  OF COMPLEMENTARY ANGLES 
• As complementary says the angle less than 90°. So here we have the trigonometry ratios of angle lying between 0 ° and 90°.

         SIN(90-A)= COS A
        COS(90-A)= SIN A
       TAN (90-A) =COTA
      COT(90-A) = TANA
      SEC(90-A)= COSECA
     COSEC(90-A) = SECA

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