Question

What is the distance between `(3 ,( pi)/4 )` and `(4 , ( pi )/2 )`?

Answer 1

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(theta)`

where `a = 3, b = 4 and theta = pi/2 - pi/4 = pi/4`

`c^2 = 3^2 +4^2 - 2(3)(4)cos(pi/4)`

`c^2 = 3^2 +4^2 - 2(3)(4)cos(pi/4)`

`c ~~ 2.8`