Thursday, May 19, 2016

What is Trigonometrical function?

 

Trigonometrical  function:In trigonometry there is importance of all thing whether it is line, angle, identities or function. Trigonometrical function has some perticular importance. If you are familiar with these function and formulas; you can easily solve problem. 



So, here, we gathered all trigonometrical function and formulas. This has been done for the easiness of students or math lover. Hope, you'll like it and suggest others to at least read once.

 
 


Reciprocal identities


 

Sin x = 1/cosec x        cos x = 1/sec x           tαn x = 1/ cot x

cosec x = 1/sin x        sec = 1/cos x               cot x = 1/tαn x



Pythagorean Identities


sin2 x + cos2 x = 1

1 + tαn2 x = sec2 x
  1 + cot2 x = cosec2 x




Quotient Identities


tαn x = sin x/ cos x,

cot x = cos x/ sin x




Co-Function Identities


sin (π/2 – x) = cos x

cos (π/2 – x) = sin x

tαn (π/2 – x) = cot x

cosec (π/2 – x) = sec  x

sec(π/2 – x) = cosec x

cot (π/2 – x) = tαn x




Even – Odd Identities

Sin (- α) = - sin α cos(- α) = cos α, tαn( - α ) = - tαn α

Cosec ( - α) = - cosec α, sec (- α) = sec α cot (- α) = - cot α




Sum – Difference formulas



sin (x + y) = sin x cosy + cos x sin y

Cos (x + y) = cos x cox y -+ sin x sin y

tan (x + y ) = tan x + tαn y/ 1-+ tan x. tan y




Double Αngle Formulas


sin (2x) = 2sin x cosx

cos (2x) = cos2 x – sin 2 x
 
              = 2cos2 x – 1 = 1 2 sin2 x

tan (2x) = 2tan x/ 1 – tan2 x/1 tan2 x





Power-Reducing / Half angle formulas



Sin2 x = 1 – cos (2x)/2

Cos2 x = 1 + cos (2x)/2

tan2 x = 1 – cos (2x)/1 + cos (2x)




Sum to Product Formulas



Sin x + sin y = 2 sin (x + y/2) cos (x – y/2)

Sin x – sin y = 2 cos (x + y/2) sin (x – y/2)

cos x + cos y = 2 cos (x + y/2) cos (x – y/2)

cos x – cos y =  – 2sin (x + y/2) sin (x – y/2)





Product to Sum Formulas



sin x.sin y = ½ [cos (x – y) – cos (x + y )]

cos x cos y = ½ [cos (x – y) + cos (x + y)]

sin x cos y = ½ [sin (x +y) + sin (x – y)]

cos x cos y = ½ [sin (x – y) – sin (x – y)]



















 



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