Math Is Fun Forum

Septimus

Guest

Exact value for an angle.

Now, this isn't as much of a question about how to find the exact value, as it is a quesiton of algebra.

I am to find the exact value of cos 105º. I'll do that by using the exact values of 60 and 45. Thus exact value of cos 60º + exact value of 45º, being the root of 2 over 2 and 1 over 2, respectivily. My question is a simple as this:

polylog

Member

Registered: 2006-09-28

Posts: 162

Re: Exact value for an angle.

Well you can write that as :

Or:

(because

)

You can write it as any of the above... I don't think there is a way to make it any simpler than those.

Last edited by polylog (2006-11-01 12:54:30)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Exact value for an angle.

There's a mistake in the second line of working there because you've started with 1/√2 instead of 1/2.

However, the question is wrong anyway, because cos 105 ≠ cos 60 + cos 45.

You need to use the addition formula, namely cos(A+B) = cosAcosB - sinAsinB.

Using 60 and 45, this gets us cos60cos45 - sin60sin45.

---

Why did the vector cross the road?
It wanted to be normal.

polylog

Member

Registered: 2006-09-28

Posts: 162

Re: Exact value for an angle.

Oops, fixed.
Thanks.
Two lessons for me: thinking more about Latex and less about algebra is bad - and: never assume the work so far is correct !