RUMUS-RUMUS TRIGONOMETRI

tg x = sin x / cos x
ctg x = cos x / sin x
csc x = 1 / sin x
sec x = 1 / cos x
ctg = 1 / tg x

sin² x + cos² x = 1
tg² x + 1 = sec² x
ctg² + 1 = csc² x 

sin 2x = 2 sin x cos x

cos 2x = cos² x - sin² x = 2 cos² x - 1 = 1 - 2 sin² x

tan 2x = (2 tan x) / (1 - tan² x)

sin 3x = 3 sin x - 4 sin³ x

cos 3x = 4 cos³ x - 3 cos x

tan 3x = (3 tan x - tan³ x)/(1 - 3 tan² x)

1 - cos x = 2 sin² ½x

1 + cos x = 2 cos² ½x

1 ± sin x = 1 ± cos (½π - x)

  

KUADRAN I 

cos (90 – x)˚ = sin x  

tg (90 – x)˚ =  ctg x

ctg (90 – x)˚ = tg x

KUADRAN II

  sin (90 + x)˚ = cos x              

  cos (90 + x)˚ = –sin x            

  tg (90 + x)˚ = –ctg x              

  ctg (90 + x)˚ = –tg x              

  sin (180 – x)˚ = sin x

  cos (180 – x)˚ = –cos x

  tg (180 – x)˚ = –tg x

  ctg (180 – x)˚ = –ctg x

KUADRAN III

  sin (180 + x)˚ = –sin x                    

cos (180 + x)˚ = –cos x          

tg (180 + x)˚ = tg x                 

  ctg (180 + x)˚ = ctg x               

  sin (270 – x)˚ = –cos x

  cos (270 - x)˚ = –sin x 

  tg (270 – x)˚ = ctg x

  ctg (270 – x)˚ = tg x 

KUADRAN IV

  sin (270 + x)˚ = –cos x  

  cos (270 + x)˚ =  sin x       

  tg (270 + x)˚ =  –ctg x      

  ctg (270 + x)˚ = –tg x      
  sin (360 – x)˚ = –sin x
  cos (360 – x)˚ = cos x 
  tg (360 – x)˚ = –tg x

  ctg (360 – x)˚ = –ctg x

  

JUMLAH DAN SELISIH DUA SUDUT
  sin (A + B) = sin A cos B + cos A sin B             

  sin (A – B) = sin A cos B – cos A sin B        

  cos (A + B) = cos A cos B – sin A sin B      

  cos (A – B) = cos A cos B + sin A. sin B 

  tg (A + B) = (tan A + tan B) / (1 – tan A tan B)

  tg (A – B) = (tan A – tan B) / (1 + tan A tan B)

PENJUMLAAN SIN, COS, dan TAN

  sin A + sin B = 2 sin ½(A + B) cos ½(A – B)

  sin A – sin B = 2 cos ½(A + B) sin ½(A – B)

  cos A + cos B = 2 cos ½(A + B) cos ½(A – B) 

  cos A – cos B = –2 sin ½(A + B) sin ½(A – B) 

  tan A + tan B = 2 sin (A + B) / {cos (A + B) + cos (A – B)}

  tan A – tan B = 2 sin (A + B) / {cos (A + B) + cos (A – B)}

PERKALIAN SIN dan COS

  2 sin A cos B = sin (A + B) + sin (A - B)

  2 cos A sin B = sin (A + B) - sin (A - B)

  2 cos A cos B = sin (A + B) + cos (A - B)

  2 sin A sin B = sin (A - B) - cos (A + B)