1 | initial version |

First, be sure to define your variable using `var('t')`

.

To find a numerical solution, you can plot the function to help identify where the roots are.

```
plot(-2*sqrt(3)*sin(t)^2+2*cos(t)*sin(t)+sqrt(3),(t,-10,10))
```

For example, to get the first positive root, you can now use `find_root`

to find the root between 0 and 3.

```
find_root(-2*sqrt(3)*sin(t)^2+2*cos(t)*sin(t)+sqrt(3),-3,3)
```

which gives 2.6179938779914944.

2 | No.2 Revision |

First, be sure to define your variable using `var('t')`

.

To find a numerical solution, you can plot the function to help identify where the roots are.

```
plot(-2*sqrt(3)*sin(t)^2+2*cos(t)*sin(t)+sqrt(3),(t,-10,10))
```

For example, to get the first positive root, you can now use `find_root`

to find the root between 0 and 3.

```
find_root(-2*sqrt(3)*sin(t)^2+2*cos(t)*sin(t)+sqrt(3),-3,3)
```

which gives 2.6179938779914944.

For an analytic solution, you can do the following:

```
solve(-2*sqrt(3)*sin(x)^2+2*cos(x)*sin(x)+sqrt(3)==0, x,to_poly_solve ='force')
```

This gives: `[x == 1/3*pi + pi*z1, x == -1/6*pi + pi*z2]`

The `z1`

and `z2`

can be any integers.

(Interestingly, I could not get the solve to work with t as the variable. I'm not sure why.)

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