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 7pi over 4. 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 0 and a theta value of 7 pi over 4. So this is going to be 0 times the cosine of 7 pi over 4. But we know that 0 times anything is just 0, so we end up with an x value of 0. Now let's see what happens with y seeing as we have that same r value of 0. Y is equal to r times the sine of theta, which, plugging those values in, is 0 times the sine of 7pi over 4. Now, again, since we are multiplying the sine of 7pi over 4 by 0, this ends up also being 0. So this point in its rectangular equivalent is 0 comma 0. 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 0, 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 0. So anytime that you have an r value of 0, your point in rectangular coordinates will actually always be your origin, 0. 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 )

15. Polar Equations

Convert Points Between Polar and Rectangular Coordinates

Precalculus

15. Polar Equations

Convert Points Between Polar and Rectangular 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

Identify the type of coordinates given. The problem provides polar coordinates, which are in the form (r, θ), where r is the radius and θ is the angle.

Understand that polar coordinates (r, θ) can be converted to rectangular coordinates (x, y) using the formulas: x = r * cos(θ) and y = r * sin(θ).

Apply the conversion formulas to the given polar coordinates. For the point (0, 7π/4), since r = 0, both x and y will be 0 regardless of the angle θ.

For the point (0, 7), again, since r = 0, both x and y will be 0 regardless of the angle θ.

For the point (-4, 0), convert using x = r * cos(θ) and y = r * sin(θ). Here, r = -4 and θ = 0, so x = -4 * cos(0) = -4 and y = -4 * sin(0) = 0, resulting in the rectangular coordinates (-4, 0).