# Lost some basic skills, working with a square root

• Oct 9th 2009, 01:17 PM
Wolvenmoon
Lost some basic skills, working with a square root
Okay, so I'm doing a TON of identities in trig, and have come to a point where I'm working on problems such as:

$\sqrt(1+cos(30))/2$

cos of 30 is $\sqrt3/2$

I've forgotten what it's called but I need a step by step guide to simplifying this! (it simplifies down to an exact answer of $\sqrt(2+\sqrt3)/2$

Edit: Yes, I've done college algebra (and aced it) but I haven't had to simplify problems like this in about 6 or 7 months, so I've lost the skill!
• Oct 9th 2009, 01:58 PM
PatrickFoster
if Cos(30) is $\frac{\sqrt{3}}{2}$ then the numerator is $\sqrt{1+\frac{\sqrt{3}}{2}}$

The 1 can be written as 2/2 and then you can factor out 1/2.

The answer you give seems to be wrong... it should have a 1/2 in the numerator under the root.
• Oct 9th 2009, 02:02 PM
Defunkt
Quote:

Originally Posted by Wolvenmoon
Okay, so I'm doing a TON of identities in trig, and have come to a point where I'm working on problems such as:

$\sqrt(1+cos(30))/2$

cos of 30 is $\sqrt3/2$

I've forgotten what it's called but I need a step by step guide to simplifying this! (it simplifies down to an exact answer of $\sqrt(2+\sqrt3)/2$

Edit: Yes, I've done college algebra (and aced it) but I haven't had to simplify problems like this in about 6 or 7 months, so I've lost the skill!

$\sqrt {\frac{1 + \frac{\sqrt{3}}{2}}{2}} = \sqrt{ \frac{ \frac{2 + \sqrt{3}}{2}}{2}} = \sqrt{ \frac{2 + \sqrt{3}}{4}}$ $= \frac{ \sqrt{2 + \sqrt{3}}}{\sqrt{4}} = \frac{\sqrt{2 + \sqrt{3}}}{2}$
• Oct 9th 2009, 02:03 PM
Wolvenmoon
Okay, so the problem is 'find the exact value of cos 15 degrees using hte half angle identity for cosine'

The example gets down to ( I think i typed it wrong) a point where it is:

The square root of (1 plus the square root of three over two) all over the square root of two.

The final answer is the square root (two plus the square root of three) all over two.

That clear it up any?
• Oct 9th 2009, 02:14 PM
Defunkt
Quote:

Originally Posted by Wolvenmoon
Okay, so the problem is 'find the exact value of cos 15 degrees using hte half angle identity for cosine'

The example gets down to ( I think i typed it wrong) a point where it is:

The square root of (1 plus the square root of three over two) all over the square root of two.

The final answer is the square root (two plus the square root of three) all over two.

That clear it up any?

The answer you gave is correct. You should note that the way you wrote the expression in your first post leaves room for confusion as to what the square root is over (it seems that you wanted to simplify $\frac{\sqrt{1 + cos(30)}}{2}$...)
• Oct 9th 2009, 03:55 PM
Wolvenmoon
Right, it's an example problem from my book. I need to know the algebra behind it as they don't show it step by step by step.

• Oct 9th 2009, 04:14 PM
Wolvenmoon
Attached is an image with exactly where my problem is highlighted. All the in book examples look the same way.

Okay, so I can't make the gimp highlight stuff. But I can't afford photoshop.
• Oct 10th 2009, 10:12 AM
Wolvenmoon
Quote:

Originally Posted by Defunkt
$\sqrt {\frac{1 + \frac{\sqrt{3}}{2}}{2}} = \sqrt{ \frac{ \frac{2 + \sqrt{3}}{2}}{2}} = \sqrt{ \frac{2 + \sqrt{3}}{4}}$ $= \frac{ \sqrt{2 + \sqrt{3}}}{\sqrt{4}} = \frac{\sqrt{2 + \sqrt{3}}}{2}$

step 2 to step 3 is where I'm having an issue. Could you elaborate on it for me?

Edit: Ugh...how is that 1 becoming a 2?

Edit 2: Oh..I see. It was being multiplied by (2/1)/2, which is 1, right?
• Oct 10th 2009, 11:08 AM
Defunkt
Quote:

Originally Posted by Wolvenmoon
step 2 to step 3 is where I'm having an issue. Could you elaborate on it for me?

Edit: Ugh...how is that 1 becoming a 2?

Edit 2: Oh..I see. It was being multiplied by (2/1)/2, which is 1, right?

Correct.

$\sqrt \frac {1 + \frac{\sqrt{3}}{2}}{2} = \sqrt \frac{\frac{2}{2} + \frac{ \sqrt{3}}{2}}{2} = \sqrt{\frac{ \frac{2 + \sqrt{3}}{2}}{2}}$