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

Answer 1

Emma Aldridge

#color(purple)("Distance between the two polar coordinates " d )color(purple)(~~ 1.8626#

Distance between tow points knowing the polar coordinates is given by the formula using cosine rule

#d = sqrt(r_1 ^2 + r_2 ^2 - 2 r_1 r_2 cos (theta_2 - theta_1)#

#"Given " r_1 = 2, r_2 = 1, theta_1 = ((12pi)/8)^c, theta_2 = (-pi/8)^c#

#d = sqrt (2^2 + 1^2 - (2 * 2 * 1 * cos (-pi/8 - (12pi)/8))#

#color(purple)(d )= sqrt (5 - 4 cos ((-13pi)/8)) color(purple)(~~ 1.8626#

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Answer 2

Paisley Johnson

The distance between the polar coordinates (2, (12π)/8) and (1, (-π)/8) is 1.

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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.