Convert the polar coordinate $\left(6, \frac{\pi}{4}\right)$ to Cartesian coordinates.
Enter exact values.
\[
x=
\]
\[
y=
\]

Answer

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Answer

The Cartesian coordinates equivalent to the given polar coordinates are approximately (4.24, 4.24)

Steps

Step 1 ：Given the polar coordinate $(6, \frac{\pi}{4})$

Step 2 ：Convert the polar coordinate to Cartesian coordinates using the formulas $x = r \cos(\theta)$ and $y = r \sin(\theta)$

Step 3 ：Substitute $r = 6$ and $\theta = \frac{\pi}{4}$ into the formulas

Step 4 ：Calculate $x = 6 \cos(\frac{\pi}{4}) = 4.24$ and $y = 6 \sin(\frac{\pi}{4}) = 4.24$

Step 5 ：The Cartesian coordinates equivalent to the given polar coordinates are approximately (4.24, 4.24)