Using radicals in trig, and their conversions

[moe11]

Homework Statement

find the exact value of cos105 deg

Homework Equations

n/a

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 could guide me through the steps or provide a link doing that. Thanks a lot everyone.

 

[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:
$$\frac{\sqrt{x}}{\sqrt{y}} = \sqrt{\frac{x}{y}}$$

 

[moe11]

I think this is what you're asking for:

Assuming x,y non-negative:

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

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

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

 

[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.

 

[Integral]

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

 

[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.

 

[moe11]

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

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

 

[moe11]

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.

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

 

[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

 

[Sjorris]

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

My bad, this is the correct link.

 

[louie3006]

Homework Statement

find the exact value of cos105 deg

Homework Equations

n/a

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 could guide me through the steps or provide a link doing that. Thanks a lot everyone.

you are on the right track, but you need to use the right formula which tells you exactly what to do and don't forget your signs according to where the angle is located and its function in that certain quadrant.
now you assign one side as (cos(45+60)= cos45cos60-sin45sin60) α &β then you need to plot them on the graph and then you go from there.