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What is the distance between the following polar coordinates?: # (-1,(pi)/2), (2,(15pi)/12) #

Answer 1

Christopher Agresta

I left explanation, try to finish it

In Euclidean geometry, we have where dl is the distance, we have: #dl^2# = #dx^2 + dy^2#

In polar coordinates: x =# r*cos(theta)# dx = #drcos(theta) - rsin(theta)d theta#

y = #r*sin(theta)# dy = #drsin(theta) + rcos(theta)d theta#

Plug into the first formula and you get the answer:)

Distance between 2 coordinates in polar coordiantes is given by: l = #sqrt((r_2-r_1)^2 + r^2(theta_1 - theta_2))#

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Answer 2

Aurora Alvarado

To find the distance between the polar coordinates ((-1, \frac{\pi}{2})) and ((2, \frac{15\pi}{12})), you can use the formula for the distance between two points in polar coordinates, which is given by:

[d = \sqrt{r_1^2 + r_2^2 - 2r_1r_2\cos(\theta_2 - \theta_1)}]

where (r_1) and (r_2) are the radii, and (\theta_1) and (\theta_2) are the angles.

For the given coordinates:

(r_1 = -1), (r_2 = 2), (\theta_1 = \frac{\pi}{2}), (\theta_2 = \frac{15\pi}{12})

Substitute these values into the formula and calculate the distance (d).

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Answer from HIX Tutor

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.