Question

What is the Cartesian form of `( -2, (-7pi)/8 )`?

Answer 1

Cartesian coordinates are

`(x, y) \equiv(1.8477, 0.765)`

Explanation:

The cartesian coordinates `(x, y)` of the given point `(r, \theta)\equiv(-2, -{7\pi}/8)` are given as

`x=r\cos\theta`

`=-2\cos({-7pi}/8)`

`=2\cos({pi}/8)`

`=1.8477`

`y=r\sin\theta`

`=-2\sin({-7pi}/8)`

`=2\sin({pi}/8)`

`=0.765`

hence the cartesian coordinates are

`(x, y) \equiv(1.8477, 0.765)`

Answer 2

Cartesian coordinates are `(1.8478,0.7654)`

Explanation:

For a polar form coordinates `(r,theta)`

Cartesian form is `(rcostheta,rsintheta)`

Hence, for `(-2,(-7pi)/8)`

Cartesian form is `(-2cos((-7pi)/8),-2sin((-7pi)/8))`

i.e. `(-2(-cos(pi/8)),-2(-sin(pi/8))`

and as `sin(pi/8)=1/2sqrt(2-sqrt2)=0.3827`

and `cos(pi/8)=1/2sqrt(2+sqrt2)=0.9239`

and Cartesian coordinates are `(1.8478,0.7654)`