# Consider the vector v = (5,8). Write v in the form (|v|cosθ|v|sinθ).

### 1 Answer | Add Yours

We need to know the magnitude of v and the angle it makes with the x-axis.

To solve for magnitude:

`|v|=sqrt(5^2+8^2)=sqrt(89)`

For the angle it makes with the x axis:

`costheta=5/sqrt(89) -> theta=58`

Therefore, the vecotr in the form `(|v|costheta,|v|sintheta)` is:

`(sqrt89cos58,sqrt89sin58)`

**Sources:**