What is the distance between the following polar coordinates?: # (5,(7pi)/4), (9,(11pi)/8) #

1 Answer
sankarankalyanam
Jul 9, 2018

#color(violet)("Distance " d ~~ 8.4592#

Explanation:

Distance between tow 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 = 5, r_2 = 9, theta_1 = ((7pi)/4)^c, theta_2 = ((11pi)/8)^c#

#d = sqrt (5^2 + 9^2 - (2 * 5 * 9 * cos ((11pi)/8 - (7pi)/4))#

#color(violet)(d )= sqrt (106 - 90 cos ((-3pi)/8)) color(violet)(~~ 8.4592#

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