What is the distance between the following polar coordinates?: (8,(5pi)/3), (1,(7pi)/4) (8,5π3),(1,7π4)
2 Answers
Jan 13, 2018
49.07 units
Explanation:
Formula for the distance between two points:
Values:
Solve with equation
Jan 13, 2018
Explanation:
"using the "color(blue)"polar version of the distance formula"
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)|)))
"let "(r_1,theta_1)=(8,(5pi)/3)" and "(r_2,theta_2)=(1,(7pi)/4)
d^2=8^2+1^2-2.8.1cos((7pi)/4-(5pi)/3)
color(white)(d^2)=65-16cos(pi/12)
rArrd=sqrt(65-16cos(pi/12))=7.0388...
rArrd~~7" to nearest whole number"