The polar coordinates of a point are given. Find the rectangular coordinates of this point.
$(- 2, \frac{7 π}{4})$
What are the rectangular coordinates of this point?
(Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

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Answer

Thus, the rectangular coordinates of the point are $(- \sqrt{2}, \sqrt{2})$ .

Steps

Step 1 ：The polar coordinates are given as $(- 2, \frac{7 π}{4})$ , where the first value is the distance from the origin (r) and the second value is the angle measured from the positive x-axis (θ).

Step 2 ：We can convert these polar coordinates to rectangular coordinates using the formulas: $x = r \cos (θ)$ and $y = r \sin (θ)$ .

Step 3 ：Substituting the given values into these formulas, we get: $x = - 2 \cos (\frac{7 π}{4})$ and $y = - 2 \sin (\frac{7 π}{4})$ .

Step 4 ：Solving these equations, we find that $x = - \sqrt{2}$ and $y = \sqrt{2}$ .

Step 5 ：Thus, the rectangular coordinates of the point are $(- \sqrt{2}, \sqrt{2})$ .

The polar coordinates of a point are given. Find the rectangular coordinates of this point.(−2,7π4)What are the rectangular coordinates of this point?(Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Answer

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The polar coordinates of a point are given. Find the rectangular coordinates of this point.
$(- 2, \frac{7 π}{4})$
What are the rectangular coordinates of this point?
(Type an ordered pair. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)