If you've taken trigonometry, you probably know about taking the sine of a number. Like $\sin 45^\circ=0.701$.
You probably also learned that $\sin$ (and $\cos$) can be found using the unit circle.

Well, did you know that the sin of any number can also be found by adding together a bunch of numbers in a particular way? That's right, the sin of a number can come from a big addition problem. The sum (or big addition problem) to find $\sin$ looks like this: $\sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...$

Using a

We've provided the factorial function for you already.

Well, did you know that the sin of any number can also be found by adding together a bunch of numbers in a particular way? That's right, the sin of a number can come from a big addition problem. The sum (or big addition problem) to find $\sin$ looks like this: $\sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...$

Using a

`for-loop`

to handle the sum, test the results of this sum for $\sin(x)$ vs. the
built in `math.sin(x)`

function. Feel free to take many more terms that just 4 in the sum.
We've provided the factorial function for you already.

`x`

using the big sum.
Type your code here:

See your results here:

You'll have to work carefully here. Here are some notes:

- In the running sum, some terms are added,
others are subtracted. We're proposing to use the variable
`c`

to keep track of when to add and when to subtract a term (even terms subtracted, odd terms added). - We're using variable
`x`

as the number "to take the sin of." - We're using the for-loop in
`i`

to run from 1,2,3.. up to the number of terms we want in our sum. Inside of the for-loop, we have`n=2*i-1`

which will cause the variable`n`

match the power of`x`

and needed factorial in any term in the sum.