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:

Distance = sqrt((Deltax)^2+(Deltay)^2)

Values:

Deltax = 8 - 1 = 7

Deltay = (5pi)/3 - (7pi)/4 = -pi/12

Solve with equation

Distance = sqrt((Deltax)^2+(Deltay)^2)

Distance = sqrt((7)^2+(-pi/12)^2)

Distance = 49.07 units

Jan 13, 2018

d~~7

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"