Question

What is the distance between the following polar coordinates?: `(8,(5pi)/3), (1,(7pi)/4)`

Answer 1

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`

Answer 2

`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"`