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

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Answer 1 · 2016-12-27T13:26:12

$4 {sin 7.5}^{o} = (\frac{1}{2} \sqrt{2 - \sqrt{2 + \sqrt{3}}})$ $4 sin7.5^o=(1/2sqrt(2-sqrt(2+sqrt3)))$

$= 4 (0.13053) = 0.5221$ $=4(0.13053)=0.5221$ , nearly.

I make r positive in the second point and read it as

$(2, \frac{3}{2} π - π) = (2, \frac{π}{2})$ $(2, 3/2pi-pi)=(2, pi/2)$

The distance PQ between $P (a, α) and Q (b, β)$ $P(a, alpha) and Q(b, beta)$ , keeping a

and b non-negative, is

$P Q = r_{P Q} = \sqrt{r_{P}^{2} + r_{Q}^{2} - 2 r_{P} r_{Q} cos (θ_{Q} - θ_{P})}$ $PQ =r_(PQ)=sqrt(r_P^2+r_Q^2-2r_Pr_Qcos (theta_Q-theta_P))$

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

$= \sqrt{8 (1 - cos (\frac{5}{12} π))}$ $=sqrt(8(1-cos(5/12pi)))$

$= \sqrt{16 {sin}^{2} (\frac{π}{24})}$ $=sqrt(16sin^2(pi/24))$

$= 4 sin (\frac{π}{24})$ $=4sin(pi/24)$

$= 4 {sin 7.5}^{o}$ $=4sin 7.5^o$

$= 4 (\frac{1}{2} \sqrt{2 - \sqrt{2 + \sqrt{3}}})$ $=4(1/2sqrt(2-sqrt(2+sqrt3)))$

$= 4 (0.13053) = 0.5221$ $=4(0.13053)=0.5221$ , nearly.2

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