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(phasor_examples)=
# Phasor examples

Recall the unit circle from trig.  The sine and cosine are generated by rotating the
unit circle counter-clockwise and reading the cosine off of the x axis and the sine
off of the  y axis.  

Note that the sine and the cosine are out of phase by an angle of 90 degrees, with the
sine leading the cosine.  That is, at any point on the circle

$$
\sin(\theta) = \cos(\theta + 90)
$$

```{code-cell} ipython3
import matplotlib.pyplot as plt
from numpy import pi
import numpy as np
```

## Phase shift of $\phi=0$

- sin(0) =0
- cos(0) = 1

```{code-cell} ipython3
fig1, axis1 =plt.subplots(1,1, subplot_kw=dict(polar=True))
theta=np.array([0.,0.])*pi/180.;
print(f"{np.cos(theta[0])=:.3},{np.sin(theta[0])=:.3}")
rho=np.array([0.,1.]);
line1=axis1.plot(theta,rho,'b-',linewidth=3);
point1=axis1.plot(0,1,'bo');
axis1.set_rticks([]);
```

## Phase shift of $\phi=30\ deg$

- sin(0) =0
- cos(0) = 1

```{code-cell} ipython3
theta=np.array([30.,30.])*pi/180.;
rho=np.array([0,1]);
line1=axis1.plot(theta,rho,'c-',lw=4);
point1=axis1.plot(theta[0],1,'co')
print(f"{np.cos(theta[0])=:.3},{np.sin(theta[0])=:.3}")
display(fig1)
```

## Phase shift of $\phi=60\ deg$

```{code-cell} ipython3
theta=np.array([60.,60.])*pi/180.;
print(f"{np.cos(theta[0])=:.3},{np.sin(theta[0])=:.3}")
rho=np.array([0,1]);
line1=axis1.plot(theta,rho,'g-',lw=4);
point1=axis1.plot(theta[0],1,'go')
display(fig1)
```

## Phase shift of $\phi=90\ deg$

```{code-cell} ipython3
theta=np.array([90.,90.])*pi/180.;
print(f"{np.cos(theta[0])=:.3},{np.sin(theta[0])=:.3}")
rho=np.array([0,1]);
line1=axis1.plot(theta,rho,'k-',lw=4);
point1=axis1.plot(theta[0],1,'ko');
axis1.set_title('phase shifts of 0, 30, 60, 90 degrees')
display(fig1)
```

```{code-cell} ipython3

```