Math Is Fun Forum

accol

Member

Registered: 2008-09-04

Posts: 1

Precalc/trig question

Hey guys, I'm taking calc 1 and was wondering if anyone could help me with 2 problems....more specifically how to solve them.

The first question is

'Evaluate without using a calculator'
tan pi/6   and  sec 3pi/4

I looked at the back of the book...the answers don't look complicated but the text itself jumped around and didn't explain how to do these.  This is the chapter 0 in the calc 1 book (so it's a precalc refresher) so it jumps through eveything assuming you know/remember it.

The second question is...

'Find the exact value....hint: half-angle identities may be helpful'

cos^2 pi/3     and   cos^2 pi/12

If anyone can explain to me how to do these that would help alot.....our calc professor is giving us a quiz tomorrow (the second day of class!!) and the first day of class was yesterday.

Thanks in Advance,
Accol

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Precalc/trig question

1. Remember that tan = sin/cos and sec = 1/cos.

2. For the first one, you should know what cos(pi/3) is.  For the second, do as they suggest and look up the half-angle identity.

In general, you should know sin and cos of 0, pi/6, pi/4, pi/3, and pi/2.  There are nice tricks to remembering these, personally I like to draw equilateral and isosceles triangles.

---

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Precalc/trig question

I used to have a bit of trouble remembering those until I realised that the sines of those five numbers could be written as √0/2, √1/2, √2/2, √3/2 and √4/2 respectively.

Same with cosines, but with the roots going from 4 to 0.

---

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