What is the distance between the following polar coordinates?: # (7,(19pi)/12), (4,(13pi)/8) #

1 Answer
sankarankalyanam
Jul 9, 2018

#color(blue)(" Distance bet. the polar coordinates " d ~~ 3.0788#

Explanation:

Distance between two points knowing the polar coordinates is given by the formula using cosine rule

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

#"Given " r_1 = 7, r_2 = 4, theta_1 = ((19pi)/12)^c, theta_2 = ((13pi)/8)^c#

#d = sqrt (7^2 +4^2 - (2 * 7 * 4* cos ((13pi)/8 - (19pi)/12))#

#color(blue)(d )= sqrt (65 - 56 cos ((pi)/24)) color(blue)(~~ 3.0788)#

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