Convert the point to rectangular coordinates. ( 0 , 7 π 4 ) (0,\frac{7\pi}{4}) ( 0 , 4 7 π )

Here we're asked to convert the point given in polar coordinates into rectangular coordinates, and the point that we're given here is zero seven pi over four. So let's go ahead and use our formulas here in order to get our x and y values. Now x is equal to r times the cosine of theta. Here we have an r value of zero and a theta value of seven pi over four. So this is going to be zero times the cosine of seven pi over four. But we know that zero times anything is just zero, so we end up with an x value of zero. Now let's see what happens with y seeing as we have that same r value of zero. Y is equal to r times the sine of theta, which, plugging those values in, is zero times the sine of seven pi over four. Now, again, since we are multiplying the sine of seven pi over four by zero, this ends up also being zero. So this point in its rectangular equivalent is zero comma zero. Now if we think about this a little bit harder, thinking about where this point in polar coordinates is located, if I have an r value of zero, we know that it's going to be located at the pole of our graph. So in order to get this point in rectangular coordinates, it should be located at the origin which is only true of the point zero zero. So anytime that you have an r value of zero, your point in rectangular coordinates will actually always be your origin zero zero. Thanks for watching and let me know if you have questions.

Convert the point to rectangular coordinates. ( 0 , 7 π 4 ) (0,\frac{7\pi}{4}) ( 0 , 4 7 π )

( 0 , 7 4 ) (0,\frac74) ( 0 , 4 7 )

( − 4 , 0 ) (-4,0) ( − 4 , 0 )

16. Parametric Equations & Polar Coordinates

Polar Coordinates

Calculus

16. Parametric Equations & Polar Coordinates

Polar Coordinates

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Multiple Choice

Convert the point to rectangular coordinates.
$(0,\frac{7\pi}{4})$

$(0,\frac74)$

$(-4,0)$

$(0,0)$

$(0,7)$

Verified step by step guidance

Step 1: Understand the problem. The given point is in polar coordinates, represented as (r, θ), where r is the radial distance from the origin and θ is the angle measured counterclockwise from the positive x-axis. The goal is to convert this point into rectangular coordinates (x, y).

Step 2: Recall the formulas for converting polar coordinates to rectangular coordinates. The formulas are: x = r * cos(θ) and y = r * sin(θ).

Step 3: Substitute the given values into the formulas. Here, r = 0 and θ = 7π/4. Since r = 0, both x and y will be 0 regardless of the value of θ.

Step 4: Verify the result. When r = 0, the point is at the origin (0, 0) in rectangular coordinates, as there is no radial distance from the origin.

Step 5: Conclude that the rectangular coordinates of the given polar point (0, 7π/4) are (0, 0).

5:32m

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Convert the point to rectangular coordinates.(0,7π4)(0,\frac{7\pi}{4})(0,47π)

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Polar Coordinates practice set

Convert the point to rectangular coordinates.
$(0,\frac{7\pi}{4})$