What is the Cartesian form of $(1,(-pi )/4)$ ?

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Answer 1 · 2017-07-21T13:48:50

$(1/sqrt2, -1/sqrt2)$

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

We can use two simple equations to get the $x$ - and $y$ -coordinates:

$x = rcostheta$

$y = rsintheta$

Here.

So we have

$x = (1)cos(-pi/4) = color(red)(1/sqrt2$

$y = (1)sin(-pi/4) = color(blue)(-1/sqrt2$

The Cartesian form is thus

$(color(red)(1/sqrt2), color(blue)(-1/sqrt2))$

What is the Cartesian form of (1,(-pi )/4)(1,(-pi )/4)?