Ano ang Cos (arcsin (-5/13) + arccos (12/13))?

Ano ang Cos (arcsin (-5/13) + arccos (12/13))?
Anonim

Sagot:

#=1#

Paliwanag:

Una gusto mong ipaalam # alpha = arcsin (-5/13) # at # beta = arccos (12/13) #

Kaya ngayon kami ay hinahanap #color (red) cos (alpha + beta)! #

# => sin (alpha) = - 5/13 "" # at # "" cos (beta) = 12/13 #

Pag-alaala: # cos ^ 2 (alpha) = 1-sin ^ 2 (alpha) => cos (alpha) = sqrt (1-sin ^ 2 (alpha)) #

# => cos (alpha) = sqrt (1 - (- 5/13) ^ 2) = sqrt ((169-25) / 169) = sqrt (144/169) = 12 /

Katulad nito, #cos (beta) = 12/13 #

# => sin (beta) = sqrt (1-cos ^ 2 (beta)) = sqrt (1- (12/13) ^ 2) = sqrt ((169-144) / 169) = sqrt (25/169) = 5/13 #

# => cos (alpha + beta) = cos (alpha) cos (beta) -sin (alpha) sin (beta) #

Pagkatapos ay palitan ang lahat ng mga halaga na nakuha ealier.

# /> cos (alpha + beta) = 12/13 * 12/13 - (- 5/13) * 5/13 = 144/169 + 25/169 = 169 /