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What is the distance between the following polar coordinates?: # (2,(3pi)/8), (7,(3pi)/8) #

Answer 1

...I was going to convert 'em to Cartesian coordinates, and calculate the distance with the Pythagorean theorem.

But it's not necessary here. You can draw a line 2 units long, along the #(3pi)/8# angle. Keep drawing another 5 units along that same angle, to mark a point 7 units out. Boom, you've got your answer: 5 units.

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Answer 2

Samantha Adkison

To find the distance between the polar coordinates ( (2, \frac{3\pi}{8}) ) and ( (7, \frac{3\pi}{8}) ), you can use the formula for the distance between two points in polar coordinates:

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

Where:

( r_1 ) and ( r_2 ) are the magnitudes (or lengths) of the radial vectors of the two points,
( \theta_1 ) and ( \theta_2 ) are the angles of the radial vectors of the two points.

Substitute the given values into the formula and calculate the distance.

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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.