Question

Does `sin180+sin45=sin225`?

Answer 1

Ehm...I do not think so...

Explanation:

I imagine the arguments in degrees so that if you plot your sin function you get:

As you can see:
`sin(180^@)=0`
while `sin(45^@)` is positive and `sin(225^@)` is negative.

I also considered the possibility to have them in radians but it doesn't work either...

Answer 2

No

Explanation:

Remember that taking the `sin` of something is a function that is unique only to that number (let's imagine that we're in a range of `0< theta < 2pi`).

So the `sin 180` is a certain value and the `sin45` is a certain value. The `sin 225` is also a separate certain value. You cannot find the `sin` of two different values, and add them up to be the `sin` of their sum.

Think of it this way:

`sqrt4 + sqrt25 = sqrt29`
`2+5=sqrt29`
`7cancel(=)sqrt29`

In the same idea, `sin` does not work that way.

Like Gio explained, the graphs are also different.

But how can you trust just plain words? Let's actually work out this problem.

`sin180` = 0

`sin(45) = sqrt2/2`

`sin225 = -sqrt2/2`

So:

`sin180 + sin45 = sin225`

`0 + sqrt2/2 cancel(=) -sqrt2/2`

And that's why you cant work with `sin` like that!