What is the distance between #(-3 ,(5 pi)/6 )# and #(5 , (11 pi )/12 )#?

1 Answer
Jim G.
May 31, 2017

#~~7.936" to 3 dec. places"#

Explanation:

#"the distance ( d ) between 2 "color(blue)"polar coordinates"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(d^2=r_1^2+r_2^2-2r_1r_2cos(theta_2-theta_1))color(white)(2/2)|)))#

#"where " (r_1.theta_1),(r_2,theta_2)" are 2 points"#

#"the points are "#

#(r_1,theta_1)=(-3,(5pi)/6),(r_2,theta_2)=(5,(11pi)/12)#

#rArrd^2=(-3)^2+5^2-(2xx-3xx5cos((11pi)/12-(5pi)/6))#

#=9+25+30cos(pi/12)#

#~~62.9777..#

#rArrd=sqrt(62.9777..)~~7.936" to 3 decimal places"#

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