Question

Suppose the vector v has magnitude 28 and makes an angle of 324∘ with the positive x-axis. (measured counterclockwise), when v is in standard position. Write v in the form v=ai+bj?

Answer 1

22.652i - 16.458j

Step-by-step explanation:

we can use a right triangle to convert from magnitude-angle to component form!

we can change 324° to -36° to make our triangle work.

we also know that in a right triangle,

x =
`rcos\theta` and y =
`rsin\theta`

where r is the hypotenuse, so we have

`28\cos36^(\circ)=\ 22.652` for our i and
`28\sin36^(\circ) =\ 16.458` for our j