What is the distance between $(3, \frac{5 π}{12})$ $(3 ,( 5 pi)/12 )$ and $(- 2, \frac{π}{2})$ $(-2 , ( pi )/2 )$ ?

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Answer 1 · 2017-01-19T16:48:08

$\sqrt{13 + 6 \sqrt{2 + \sqrt{3}}} = 4.959$ $sqrt(13+6sqrt(2+sqrt3))=4.959$ , nearly.

Mark A (3, 5/12pi) and B (2, pi/2) that is same as B (2, -pi/2)#.

In the $△ A O B, O A = 3, O B = 2 and$ $triangle AOB, OA =3, OB = 2 and$

the anticlockwise $∠ B O A = \frac{5}{12} π - (- \frac{π}{12}) = \frac{11}{12} π$ $angle BOA=5/12pi-(-pi/12)=11/12pi$ .

Now,

$A B = \sqrt{{(O A)}^{2} + {(O B)}^{2} - 2 (O A) (O B) cos ∠ B O A}$ $AB=sqrt((OA)^2+(OB)^2-2(OA)(OB)cos angleBOA)$

$- \sqrt{3^{2} + 2^{2} - 2 (3) (2) cos (\frac{11}{12} π)}$ $-sqrt(3^2+2^2-2(3)(2)cos(11/12pi))$

$= \sqrt{13 + 12 \frac{cos π}{12}})$ $=sqrt(13+12cospi/12))$

$= q r t (13 + 12 \sqrt{\frac{1}{2} (1 + cos (\frac{π}{6}))}$ $=qrt(13+12sqrt(1/2(1+cos(pi/6))$

$= \sqrt{13 + 6 \sqrt{2 + \sqrt{3}}} = 4.959$ $=sqrt(13+6sqrt(2+sqrt3))=4.959$ , nearly.

What is the distance between (3,5π12)(3 ,( 5 pi)/12 ) and (−2,π2)(-2 , ( pi )/2 )?