Question

How do you use sum or difference identities to find the exact value of Sin 160 degrees?

Answer 1

I don't believe that you can get the exact value of `sin160^@ = sin 20^@` using the special angles.

Explanation:

`20` cannot be the result of addition or subtraction of the special angle whose exact trigonometric values are known.

In order to get the exact value of `sin160^@ = sin 20^@`, we woul d have to be able to do that.

Here's what I recall from my exposure to Galois Theory:

The `20^@` angle cannot be constructed with compass and (unmarked) straight edge.

The special angles can be constructed with compass and starightedge. And any angle that is the result of adding, subtratcing or bisecting a constructed angle can be constructed.

Building the `20^@` alngle from the special angles so that we can get the exact value of `sin20^@` would involve exactly that. Which we cannot do.