Question

What is the distance between `(4, pi/2 )` and `(5, pi/12 )`?

Answer 1

≈ 5.54

Explanation:

Using the Polar version of the `color(blue)" distance formula "`

`color(red)(|bar(ul(color(white)(a/a)color(black)( d^2 = r_1^2 + r_2 ^2 - (2r_1r_2 cos(theta_2 - theta_1)))color(white)(a/a)|)))`
where `(r_1,theta_1)" and " (r_2,theta_2)" are 2 polar points "`

let `(r_1,theta_1)=(5,pi/12)" and " (r_2,theta_2)=(4,pi/2)`

`d^2=5^2+4^2-(2xx5xx4xxcos(pi/2-pi/12)`

`=25+16-(40cos((5pi)/12)=41-(10.353)=30.647`

now `d^2=30.647 rArr d=sqrt30.647 ≈ 5.54`