# How do you find the rectangular coordinates of the point whose spherical coordinates are #(4, 3π/4, π/3)#?

The formulas are:

So:

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To find the rectangular coordinates (x, y, z) of a point given its spherical coordinates (r, θ, φ), we use the following formulas:

[ x = r \sin(φ) \cos(θ) ] [ y = r \sin(φ) \sin(θ) ] [ z = r \cos(φ) ]

Given the spherical coordinates (4, ( \frac{3π}{4} ), ( \frac{π}{3} )), we substitute these values into the formulas:

[ x = 4 \sin\left(\frac{π}{3}\right) \cos\left(\frac{3π}{4}\right) ] [ y = 4 \sin\left(\frac{π}{3}\right) \sin\left(\frac{3π}{4}\right) ] [ z = 4 \cos\left(\frac{π}{3}\right) ]

After evaluating these expressions, we obtain the rectangular coordinates of the point.

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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.

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

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