Question

What are the components of the vector between the origin and the polar coordinate `(-7, (5pi)/4)`?

Answer 1

The `x` component is `-7cos((5pi)/4)`
The `y` component is `-7sin((5pi)/4)`

Explanation:

For any polar coordinate vector, the first term is the magnitude, and the second term is the direction. The components are calculated using `sin` and `cos` of the angle, scaled to the size of the magnitude.

In this case, the magnitude is -7, and the angle is `(5pi)/4`, which is midway through the lower left quadrant, where both `x` and `y` are negative. The answers, in this case, will actually be positive because we are multiplying the sin and cos values by a negative number.

`sin((5pi)/4) = -1/sqrt2` and
`cos((5pi)/4) = -1/sqrt2`

So the answer to both components is `7/sqrt2`