Wie groß ist der Abstand zwischen den folgenden Polarkoordinaten ?: (7, (5pi) / 4), (2, (9pi) / 8)

Antworten:

# P_1P_2 = sqrt (53-28cos ((pi) / 8)) ~~ 5.209 #

Erläuterung:

# P_1P_2 = sqrt (r_1 ^ 2 + r_2 ^ 2-2r_1r_2cos (theta_2-theta_1)) #

# r_1 = 7, theta_1 = (5pi) / 4; r_2 = 2, theta_2 = (9pi) / 8 #

# P_1P_2 = sqrt (7 ^ 2 + 2 ^ 2-2 * 7 * 2cos ((9pi) / 8- (5pi) / 4)) #

# P_1P_2 = sqrt (49 + 4-28cos (- (pi) / 8) #

# P_1P_2 = sqrt (53-28cos ((pi) / 8)) ~~ 5.209 #

Antworten:

# s ~ = 5,27 #

Erläuterung:

# r_1 = 7 #

# r_2 = 2 #

# theta_1 = (5pi) / 4 #

# theta_2 = (9pi) / 8 #

# theta_2-theta_1 = (9pi) / 8- (5pi) / 4 = (9pi-10pi) / 8 = -pi / 8 #

#cos (-pi / 8) = 0,9 #

# s = sqrt (r_1 ^ 2 + r_2 ^ 2-2 * r_1 * r_2 * cos (theta_2-theta_1)) #

# s = sqrt (7 ^ 2 + 2 ^ 2-2 * 7 * 2 * 0,9) #

# s = sqrt (49 + 4-28 * 0,9) #

# s = sqrt (53-25.2) #

# s = sqrt (27,8) #

# s ~ = 5.27 #