# How do we plot magnitude-angle vector in Mathematica?

I am lost on how to plot this fairly simple vector with a magnitude and an angle in Mathematica. Any help would be appreciated. Thanks in advance.

e.g. 20 @ 50 Degree Angle

You can use the function AnglePath:

{x, y} = {0, 0};
r = 20;
t = 50 Degree;
Graphics[{Red, Arrow @ AnglePath[{x, y}, {{r, t}}]}] Alternatively, you can use AngleVector:

Graphics[{Red, Arrow[{{x, y}, AngleVector[{r, t}]}]}]


same picture

With

{r, t} = {20, 50 Degree}


You can always make the vector mathematically with

vec = r {Cos@t, Sin@t}


and an illustrative example

With[
{pt = r {Cos@t, Sin@t}(*Mathematical implementation of the vector*)},
Graphics[
{
(*Make all the lines thick*) Thickness[.007],
(*The arrow itself*){Arrow@{{0, 0}, pt}},
(*Arc to show label the angle*) {Circle[{0, 0}, 5, {0, 50 Degree}]},
(*Angle label*) {Text[Style[θ == 50 Degree, 15], 4 {0.85 Cos[t/2.5], 1.1 Sin[t/2.5]}]},
(*Magnitude label*) {Text[Style["r = 20", 15], pt {0.9, 1}]}
}
]
] 