How to Simplify an Acute Angle Solution Using Algebra?

[number0]

Homework Statement

Let u=3i+0j+k and v=i-2j+k have a common tail. Let $$\theta$$ be the acite angle

between u and v. Calculus sin$$\theta$$

Homework Equations

ll u x v ll = ll u ll ll v ll sin$$\theta$$

The Attempt at a Solution

First of all, I solved the problem already. To save time, I will not show my work, but show

the answer I computed:

sin$$\theta$$ = $$\frac{\sqrt{44}}{\sqrt{10}\sqrt{6}}$$

Which is equivalent to my textbook's answer:

sin$$\theta$$ = $$\sqrt{\frac{11}{15}}$$

Now my question is how do I transform the answer I computed to the textbook's answer? I

am pretty sure that it has to do with the concept of acute angles. Can anyone please

explain this to me? Thanks.

 

[rock.freak667]

√a√b = √ab

√a/√b = √(a/b)

 

[Office_Shredder]

An acute angle is just one that is between 0 and $$\frac{\pi}{2}$$. Draw a pair of lines forming a (smallish) angle. There are two angles really formed, the obvious small one between them, and the huge one that's about 300 degrees on the other side.

 

[number0]

An acute angle is just one that is between 0 and $$\frac{\pi}{2}$$. Draw a pair of lines forming a (smallish) angle. There are two angles really formed, the obvious small one between them, and the huge one that's about 300 degrees on the other side.

Hmmm, I see. But, I still do not know how to convert an obtuse angle to an acute angle. So

let's pretend that I have a an angle, say:

cos$$\theta$$ = $$\frac{-10}{\sqrt{22}\sqrt{42}}$$.

How do I go about converting this angle into an acute angle without using a calculator?

 

[vela]

First of all, I solved the problem already. To save time, I will not show my work, but show

the answer I computed:

sin$$\theta$$ = $$\frac{\sqrt{44}}{\sqrt{10}\sqrt{6}}$$

Which is equivalent to my textbook's answer:

sin$$\theta$$ = $$\sqrt{\frac{11}{15}}$$

Now my question is how do I transform the answer I computed to the textbook's answer? I

am pretty sure that it has to do with the concept of acute angles. Can anyone please

explain this to me? Thanks.

It has nothing to do with the concept of acute angles. It's just algebra. Use the rules rock.freak posted to simplify the expression.