What is the distance between $(3, \frac{π}{4})$ $(3 ,( pi)/4 )$ and $(4, \frac{π}{2})$ $(4 , ( pi )/2 )$ ?

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What is the distance between $(3, \frac{π}{4})$ $(3 ,( pi)/4 )$ and $(4, \frac{π}{2})$ $(4 , ( pi )/2 )$ ?

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Answer 1 · 2017-01-17T21:17:19

Use a variant of The Law of Cosines

Explanation:

The distance is one side of a triangle with the other two sides being the two given radii, 3 and 4, and the angle between them the difference of the two angles. This allows us to use the The Law of Cosines :

$c^{2} = a^{2} + b^{2} - 2 (a) (b) cos (θ)$ $c^2 = a^2 + b^2 - 2(a)(b)cos(theta)$

where $a = 3, b = 4 and θ = \frac{π}{2} - \frac{π}{4} = \frac{π}{4}$ $a = 3, b = 4 and theta = pi/2 - pi/4 = pi/4$

$c^{2} = 3^{2} + 4^{2} - 2 (3) (4) cos (\frac{π}{4})$ $c^2 = 3^2 +4^2 - 2(3)(4)cos(pi/4)$

$c \approx 2.8$ $c ~~ 2.8$

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What is the distance between $(3, \frac{π}{4})$ $(3 ,( pi)/4 )$ and $(4, \frac{π}{2})$ $(4 , ( pi )/2 )$ ?

1 Answer

Explanation:

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