What is the Cartesian form of $(4, \frac{5 π}{2})$ $( 4, (5pi)/2 )$ ?

Question

What is the Cartesian form of $(4, \frac{5 π}{2})$ $( 4, (5pi)/2 )$ ?

1 Answer

Impact of this question

2051 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-17T22:46:17

The point is $(0, 4)$ $(0,4)$ .

Explanation:

The standard conversion between polar and cartesian coordinates is:
$x = r cos (θ)$ $x = r cos(theta)$
$y = r sin (θ)$ $y = r sin(theta)$

The given coordinates are of the form $(r, θ)$ $(r, theta)$ . And one will also note that:
$\frac{5 π}{2} = \frac{π}{2} + 2 π$ $(5pi)/2 = pi/2 + 2pi$

Meaning that we can simply reduce the angle to $\frac{π}{2}$ $pi/2$ since we can always subtract full revolutions of the unit circle from angles in polar coordinates, so the result is:
$x = 4 cos (\frac{π}{2}) = 0$ $x = 4cos((pi)/2) = 0$
$y = 4 sin (\frac{π}{2}) = 4$ $y = 4sin((pi)/2) = 4$

The point, then, is $(0, 4)$ $(0,4)$

Science

Math

Humanities

... and beyond

What is the Cartesian form of $(4, \frac{5 π}{2})$ $( 4, (5pi)/2 )$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the Cartesian form of (4,5π2)( 4, (5pi)/2 ) ?

1 Answer

Explanation:

Related questions

Impact of this question

What is the Cartesian form of $(4, \frac{5 π}{2})$ $( 4, (5pi)/2 )$ ?