Vector Coordinates

Question

I need to plot a vector onto a Cartesian plane. I have the vector magnitude and the vector angle, in relation to the y-axis (which can be larger than 90°). One of the ends of the vector will always be at $(0, 0)$. How can I calculate the coordinates for the other end of the vector?

Answer 1

Think about forming a triangle with respect to the y-axis. Then use basic geometric equations for the coordinates.

Look at this image:

You were provided C, and the angle from B to C. This is just a simple triangle. To find the coordinates, you are simply finding B and A. These can be found by:

$$A=Csin(\theta)$$ $$B=Ccos(\theta)$$

Answer 2

Hint:$$\sin(\theta)= \frac{\text{opposite}}{\text{hypotenuse}}$$