What is the Cartesian form of $(49,(3pi)/4)$ ?

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Answer 1 · 2017-07-02T10:05:15

$(-49/(sqrt(2)), 49/(sqrt(2)))$

We're asked to find the rectangular (Cartesian) coordinate of a given polar coordinate.

This can be done using the formulas

$x = rcostheta$

$y = rsintheta$

Therefore,

$x = 49cos((3pi)/4) = color(red)(-49/(sqrt(2))$

$y = 49cos((3pi)/4) = color(blue)(49/(sqrt(2))$

which are the exact values.

The equivalent Cartesian coordinate is thus

$(color(red)(-49/(sqrt(2))), color(blue)(49/(sqrt(2))))$

What is the Cartesian form of (49,(3pi)/4)(49,(3pi)/4)?