대답:
#sin (a + b) = 56 / 65 #
설명:
주어진, # tana = 4 / 3 및 cotb = 5 / 12 #
# rarrcota = 3 / 4 #
# rarrsina = 1 / csca = 1 / sqrt (1 + cot ^ 2a) = 1 / sqrt (1+ (3/4) ^ 2) = 4 / 5 #
# rarrcosa = sqrt (1-sin ^ 2a) = sqrt (1- (4/5) ^ 2) = 3 / 5 #
# rarrcotb = 5 / 12 #
1 / sqrt (1 + cot ^ 2b) = 1 / sqrt (1+ (5/12) ^ 2) = 12 / 13 #
# rarrcosb = sqrt (1-sin ^ 2b) = sqrt (1- (12/13) ^ 2) = 5 / 13 #
지금, #sin (a + b) = sina * cosb + cosa * sinb #
#=(4/5)(5/13)+(3/5)*(12/13)=56/65#
대답:
#sin (a + b) = 56 / 65 #
설명:
이리, # 0 ^ circ <color (보라색) (a) <90 ^ circ => I ^ (st) 사분면 => 색상 (파랑) (All, fns.
# 0 ^ circ <color (바이올렛) (b) <90 ^ circ => I ^ (st) 사분면 => color (blue) (All, fns.> 0 #
그래서, # 0 ^ circ <color (보라색) (a + b) <180 ^ circ => I ^ (st)와 II ^ (nd) 사분면 #
# => 색상 (파랑) (죄 (a + b)> 0 #
지금, # tana = 4 / 3 => seca = + sqrt (1 + tan ^ 2a) = sqrt (1 + 16 / 9) = 5 / 3 #
#:. color (빨강) (cosa) = 1 / seca = color (빨강) (3 / 5 #
# => color (red) (sina) = + sqrt (1-cos ^ 2a) = sqrt (1-9 / 25) = color (빨강) (4 / 5 #
또한, # cotb = 5 / 12 => cscb = + sqrt (1 + cot ^ 2b) = sqrt (1 + 25 / 144) = 13 / 12 #
#:. 컬러 (적색) (sinb) = 1 / cscb = 컬러 (적색) (12 / 13 #
# => 색상 (적색) (cosb) = + sqrt (1-sin ^ 2b) = sqrt (1-144 / 169) = 색상 (적색) (5 / 13 #
금후, #sin (a + b) = sinacosb + cosasinb #
# => sin (a + b) = 4 / 5xx5 / 13 + 3 / 5xx12 / 13 #
#sin (a + b) = 20 / 65 + 36 / 65 = 56 / 65 #
