Hvordan beregner du synd (2sin ^ -1 (10x))?

Svar:

#sin (2sin ^ (- 1) (10x)) = 20xsqrt (1-100x ^ 2) #

Forklaring:

# "La" y = sin (2sin ^ (- 1) (10x)) #

Nå, la # "" theta = sin ^ (- 1) (10x) "" => synd (theta) = 10x #

# => Y = sin (2teta) = 2sinthetacostheta #

Husk det: # "" cos ^ 2theta = 1-sin ^ 2theta => costheta = sqrt (1-sin ^ 2theta) #

# => Y = 2sinthetasqrt (1-sin ^ 2teta) #

# => Y = 2 * (10x) sqrt (1- (10x) ^ 2) = farge (blå) (20xsqrt (1-100x ^ 2)) #

Hvordan beregner du synd ((13pi) / 6)?

Sin ((13pi) / 6) = sin (2 pi + pi / 6) = sin (pi / 6) = 1/2

Bevis: - synd (7 theta) + synd (5 theta) / synd (7 theta) -sin (5 theta) =?

(sin7x + sin5x) / (sin7x-sin5x) = tan6x * cotx rarr (sin7x + sin5x) / (sin7x-sin5x) = (2sin ((7x + 5x) / 2) * cos ((7x-5x) / 2) ) / (2x (5x) / 2) * cos ((7x + 5x) / 2) = (sin6x * cosx) / (sinx * cos6x) = (tan6x) / tanx = tan6x * cottx

Hvordan beregner du synd (cos ^ -1 (5/13) + tan ^ -1 (3/4))?

Synd (cos ^ (- 1) (5/13) + tan ^ (- 1) (3/4)) = 63/65 La cos ^ (- 1) (5/13) = x deretter rarrcosx = 5/13 rarrsinx = sqrt (1-cos ^ 2x) = sqrt (1- (5/13) ^ 2) = 12/13 rarrx = sin ^ (- 1) (12/13) = cos ^ (- 1) 13) La også tan ^ (- 1) (3/4) = y da rarrtany = 3/4 rarrsiny = 1 / cscy = 1 / sqrt (1 + cot ^ 2y) = 1 / sqrt (1+ 3 - 5) = 3/5 rarry = tan ^ (- 1) (3/4) = sin ^ (- 1) (3/5) rarrcos ^ (- 1) (5/13) + tan ^ 1) (3/4) = sin ^ (- 1) (12/13) + sin ^ (- 1) (3/5) = sin ^ (- 1) (12/13 * 5) ^ 2) + 3/5 * sqrt (1- (12/13) ^ 2)) = sin ^ (- 1) (12/13 * 4/5 + 3/5 * 5/13) = 63 / 65 Nå, synd (cos ^ (- 1) (5/13) + tan ^ (- 1) (3/