# What is the distance between the following polar coordinates?: # (5,(7pi)/4), (3,(9pi)/8) #

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To find the distance between the polar coordinates (5, (7π)/4) and (3, (9π)/8), you can use the distance formula in polar coordinates, which is given by:

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

Plugging in the values, the distance between the two points is:

[ \sqrt{5^2 + 3^2 - 2(5)(3)\cos\left(\frac{9\pi}{8} - \frac{7\pi}{4}\right)} ]

[ = \sqrt{25 + 9 - 30\cos\left(\frac{9\pi}{8} - \frac{7\pi}{4}\right)} ]

[ = \sqrt{34 - 30\cos\left(\frac{9\pi}{8} - \frac{7\pi}{4}\right)} ]

[ = \sqrt{34 - 30\cos\left(\frac{\pi}{8}\right)} ]

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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.

- What is the Cartesian form of #(-9,(5pi )/4)#?
- What is the distance between the following polar coordinates?: # (3,(-5pi)/12), (6,(3pi)/8) #
- What is the arclength of #r=-3cos(theta/16+(pi)/16) # on #theta in [(-5pi)/16,(9pi)/16]#?
- What is the equation of the tangent line to the polar curve # f(theta)=theta^2cos(3theta)-thetasin(2theta)+tan(theta/6) # at #theta = pi#?
- What is the Cartesian form of #( -9, (-7pi)/3 ) #?

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