Asked by Lizzie
Find the distance between the points with polar coordinates (2, 120°) and (1, 45°)
Answers
Answered by
Reiny
there is a formula that says:
distance between two points (r1,Ø1) and (r2,Ø2) , where both are in polar form is
√ [ r1^2 + r2^2 - 2(r1)(r2)cos(Ø2-Ø1) }
= √ [ 4 + 1 - 2(2)(1)cos(120-45) ]
= √ [ 5 - 4cos75]
= √[ 5 - (√6 - √2)/4] ----> exact value, or
= appr. 1.99
or
you could convert them to cartesian form
(2, 120°) = (-1,√3)
(1,45°) = (√2/2 , √2/2)
distance = √[ (√2/2 + 1)^2 + (√2/2 - √3)^2 ]
= 1.99
distance between two points (r1,Ø1) and (r2,Ø2) , where both are in polar form is
√ [ r1^2 + r2^2 - 2(r1)(r2)cos(Ø2-Ø1) }
= √ [ 4 + 1 - 2(2)(1)cos(120-45) ]
= √ [ 5 - 4cos75]
= √[ 5 - (√6 - √2)/4] ----> exact value, or
= appr. 1.99
or
you could convert them to cartesian form
(2, 120°) = (-1,√3)
(1,45°) = (√2/2 , √2/2)
distance = √[ (√2/2 + 1)^2 + (√2/2 - √3)^2 ]
= 1.99
Answered by
Reiny
notice that the formula I gave is just a variation of the Cosine Law formula.
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