What is the Cartesian form of $(4, \frac{11 π}{4})$ $( 4 , ( 11pi)/4 )$ ?

Question

What is the Cartesian form of $(4, \frac{11 π}{4})$ $( 4 , ( 11pi)/4 )$ ?

1 Answer

Impact of this question

1210 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-22T21:59:24

$(- 2 \sqrt{2}, 2 \sqrt{2})$ $(-2sqrt2 , 2sqrt2 )$

Explanation:

Using the formulae that links Polar to Cartesian coordinates.

$∙ x = r cos θ$ $• x = rcostheta$

$∙ y = r sin θ$ $• y = rsintheta$

here r = 4 and $θ = \frac{11 π}{4}$ $theta = (11pi)/4$
$---------------------------------------------------$ $"---------------------------------------------------"$
$\Rightarrow x = 4 cos (\frac{11 π}{4}) = 4 cos (\frac{11 π}{4} - 2 π) = cos (\frac{3 π}{4})$ $rArr x = 4cos((11pi)/4) = 4cos((11pi)/4 - 2pi) = cos((3pi)/4)$

and $cos (\frac{3 π}{4}) = - cos (\frac{π}{4}) = - \frac{1}{\sqrt{2}}$ $cos((3pi)/4) = -cos(pi/4) = - 1/sqrt2$
thus $x = 4 \times \frac{- 1}{\sqrt{2}} = - 2 \sqrt{2}$ $x = 4xx(-1)/sqrt2 = - 2sqrt2$
$-------------------------------------------------$ $"-------------------------------------------------"$

$\Rightarrow y = 4 sin (\frac{11 π}{4}) = 4 sin (\frac{π}{4}) = 4 \times \frac{1}{\sqrt{2}} = 2 \sqrt{2}$ $rArr y = 4sin((11pi)/4) = 4sin(pi/4) = 4xx1/sqrt2 = 2sqrt2$

Science

Math

Humanities

... and beyond

What is the Cartesian form of $(4, \frac{11 π}{4})$ $( 4 , ( 11pi)/4 )$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the Cartesian form of (4,11π4)( 4 , ( 11pi)/4 ) ?

1 Answer

Explanation:

Related questions

Impact of this question

What is the Cartesian form of $(4, \frac{11 π}{4})$ $( 4 , ( 11pi)/4 )$ ?