What is the distance between the following polar coordinates?: # (1,(-5pi)/12), (8,(5pi)/8) #
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To find the distance between the given polar coordinates, we'll use the formula for the distance between two points in polar coordinates:
( d = \sqrt{(r_2^2 + r_1^2 - 2r_1r_2\cos(\theta_2 - \theta_1))} )
Substituting the given values:
( d = \sqrt{(8^2 + 1^2 - 2(8)(1)\cos\left(\frac{5\pi}{8} - \frac{-5\pi}{12}\right))} )
( d = \sqrt{(64 + 1 - 16\cos(\frac{5\pi}{8} + \frac{5\pi}{12}))} )
( d = \sqrt{(65 - 16\cos(\frac{15\pi}{24} + \frac{10\pi}{24}))} )
( d = \sqrt{(65 - 16\cos(\frac{25\pi}{24}))} )
( d ≈ \sqrt{(65 - 16\cos(\frac{\pi}{24}))} )
( d ≈ \sqrt{(65 - 16\cos(15))} )
( d ≈ \sqrt{(65 - 16 \cdot 0.9659)} )
( d ≈ \sqrt{(65 - 15.4544)} )
( d ≈ \sqrt{49.5456} )
( d ≈ 7.04 )
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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.
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.
- How do you find the slope of the polar curve #r=1+sin(theta)# at #theta=pi/4# ?
- What is the distance between the following polar coordinates?: # (4,(7pi)/4), (3,(3pi)/8) #
- How do you find the equation of the tangent lines to the polar curve #r=sin(2theta)# at #theta=2pi# ?
- How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3(1-costheta)#?
- What is the polar form of #(1,3)#?

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