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What is the distance between the following polar coordinates?: # (2,(pi)/4), (3,(13pi)/8) #

Answer 1

#d = 4.90781#

First we pass the points in polar coordinates to Cartesian. The pass equations are #x = r cos(theta)# #y = r sin(theta)# #(2,pi/2)->(2 cos(pi/2),2 sin(pi/2))=(0,2) = (x_1,y_1)# #(3,(13pi)/8)->(3 cos((13pi)/8),3 sin((13pi)/8)) =(1.14805, -2.77164) = (x_2,y_2)# Now we calculate the distance #d = sqrt((x_1-x_2)^2+(y_1-y_2)²) = 4.90781#

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Answer 2

Samantha Adkison

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

[ 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 polar coordinates, and ( \theta_1 ) and ( \theta_2 ) are the angles.

For the given polar coordinates:

( r_1 = 2 )
( r_2 = 3 )
( \theta_1 = \frac{\pi}{4} )
( \theta_2 = \frac{13\pi}{8} )

Plug these values into the formula to find 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.