# What is the distance between the following polar coordinates?: # (7,(-2pi)/3), (5,(-pi)/6) #

It's probably easiest to do this by first converting your polar coordinates into Cartesian coordinates—of course, polar coordinates are non-unique so theoretically they could translate to different Cartesian coordinates. We shall take the obvious set of points, however.

With a bit of further calculation:

With a further bit of calculation:

The final answer after inserting those numbers is:

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To find the distance between two polar coordinates (r₁, θ₁) and (r₂, θ₂), you can use the formula:

Distance = √(r₁² + r₂² - 2*r₁*r₂*cos(θ₂ - θ₁))

Substitute the given values into the formula:

r₁ = 7, θ₁ = -2π/3 r₂ = 5, θ₂ = -π/6

Distance = √(7² + 5² - 2*7*5*cos((-π/6) - (-2π/3)))

Distance = √(49 + 25 - 70*cos(π/3))

Distance = √(49 + 25 - 70*(1/2))

Distance = √(49 + 25 - 35)

Distance = √39

So, the distance between the two polar coordinates is √39.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- What is the distance between the following polar coordinates?: # (2,(12pi)/8), (1,(-pi)/8) #
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- What is the polar form of #( -4,-2 )#?

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