# Using radicals in trig, and their conversions

1. Dec 2, 2008

### moe11

1. The problem statement, all variables and given/known data
find the exact value of cos105 deg

2. Relevant equations
n/a

3. The attempt at a solution
i know up to

cos(45+60)= cos45cos60-sin45sin60
i get lost with the converstions to radical numbers, for example sgrt(2/2) or sqrt2.
how do i convert into radicals, and how do i convert out of out of them. once i know that, i can finish solving.

I was wondering if someone coud guide me through the steps or provide a link doing that. Thanks alot everyone.

2. Dec 2, 2008

### kidmode01

I think this is what you're asking for:

Assuming x,y non-negative:

Product rule:
$$\sqrt{x}\sqrt{y} = \sqrt{xy}$$

Quotient rule:
$$\frac{\sqrt{x}}{\sqrt{y}} = \sqrt{\frac{x}{y}}$$

3. Dec 2, 2008

### moe11

your close, but thats not really what im looking for. basically if you were trying to solve that problem, where would you go from where i left it?

4. Dec 3, 2008

### Tedjn

I'm afraid I don't understand what you are looking for from us. If it were me, I would replace each of the sine and cosines by their corresponding radical values and then simplify. You should know what the values are from the special 45-45-90 and 30-60-90 right triangles.

5. Dec 3, 2008

### Integral

Staff Emeritus
You should have memorized the value of things like sin(45), cos(45), sin(60), cos(60) simply replace the trig function with its value at the specified point. You should also memorize the radian value of angles in degrees.

so you should know:

45deg = $\frac {\pi} 4$

and that:

Sin(45) = sin $( \frac {\pi} 4) = \frac { \sqrt {2}} 2$

6. Dec 3, 2008

### Sjorris

Exact values for certain simple angles (including the ones you are looking for) can be found here. You can also derive them geometrically by drawing triangles and using Pythagoras' law.

7. Dec 3, 2008

### moe11

yes thank you, thats what i need to know, how do you go from pi/4 to the radical? or any other radian measure to a radical?

8. Dec 3, 2008

### moe11

your link doesn't seem to work, if yo ucould provide me with it im sure it will help a lot. thank you.

9. Dec 3, 2008

### kidmode01

I hate to redirect you away from physics forums but the Wikipedia article on the unit circle contains a picture of the unit circle with the values your looking for with an explanation of why they are in the form (cos(t),sin(t)).

ie:

cos(60) = cos(pi/3) = 1/2

http://en.wikipedia.org/wiki/Unit_circle

10. Dec 3, 2008