# What is the distance between the following polar coordinates?: # (5,(-5pi)/3), (5,(11pi)/6) #

Before finding the distance between these points, it is necessary to convert them to rectangular coordinates. These points have been plotted as in the given figure and explained as follows:

To plot the point

To plot the point

Distance between points P and Q=

=

= 5

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To find the distance between two polar coordinates, you can use the formula:

Distance = sqrt(r1^2 + r2^2 - 2 * r1 * r2 * cos(θ2 - θ1))

Given: r1 = 5, θ1 = -5π/3 r2 = 5, θ2 = 11π/6

Substituting the values: Distance = sqrt(5^2 + 5^2 - 2 * 5 * 5 * cos((11π/6) - (-5π/3)))

Calculate cos((11π/6) - (-5π/3)): = cos(11π/6 + 5π/3) = cos(11π/6 + 10π/6) = cos(21π/6) = cos(7π/2) = 0

Substitute back into the formula: Distance = sqrt(5^2 + 5^2 - 2 * 5 * 5 * 0) = sqrt(25 + 25 - 0) = sqrt(50) = 5√2

Therefore, the distance between the given polar coordinates is 5√2.

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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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