Was ist cos (sin ^ -1 (0.5))?

Was ist cos (sin ^ -1 (0.5))?
Anonim

Antworten:

#cos (sin ^ (-1) (0.5)) = sqrt (3) / 2 #

Erläuterung:

Lassen #sin ^ (- 1) (0,5) = x # dann

# rarrsinx = 0.5 #

# rarrcosx = sqrt (1-sin ^ 2x) = sqrt (1-0,5 ^ 2) = sqrt (1- (1/2) ^ 2) = sqrt (3) / 2 #

# rarrx = cos ^ (-1) (sqrt3 / 2) = sin ^ (-1) (0,5) #

Jetzt, #rarrcos (sin ^ (-1) (0.5)) = cos (cos ^ (-1) (sqrt3 / 2)) = sqrt (3) / 2 #