Question

What is the Cartesian form of `( -7 , (-3pi)/4 )`?

Answer 1

The cartesian equivalent is `((7sqrt(2))/2,(7sqrt(2))/2)`.

Explanation:

In polar we have:
`x = r*cos(\theta)`
`y = r*sin(\theta)`

In the given ordered pair `r=-7` and `theta=-(3pi)/4`.

Substituting gives:
`x=-7cos(-(3pi)/4) = -7(-sqrt(2)/2)=(7sqrt(2))/2`
`y=-7sin(-(3pi)/4) = -7(-sqrt(2)/2)=(7sqrt(2))/2`

So the cartesian equivalent is `((7sqrt(2))/2,(7sqrt(2))/2)`.