Picture is attached below. PLEASE show me how to solve this.

Question

anonymous · Answer

attachment

geerky42 · Answer

who the flutter chose colors like this? it hurts my eyes...

anonymous · Answer

use calculator and it is solved 
shift cos then divide by 2 and so on

whitemonsterbunny17 · Answer

LOL! @geerky42 I was thinking the same thing! xD

anonymous · Answer

i dont know if it is correct but i think that the answer is 0.948683...

imstuck · Answer

You need to actually plot this using the cosine identity.  Do you know how to do that?

anonymous · Answer

ya i think the program wants me to use this equation

imstuck · Answer

BTW the sin of an angle is not represented as .948683.  You need it as a fraction.  In Q2 this is what the angle looks like:

imstuck · Answer

|dw:1404352338662:dw|

imstuck · Answer

when you solve for x you are solving for the side opposite the angle, which is what you need when you find the sin of the angle.  Sin theta = side opposite / hypotenuse.

anonymous · Answer

attachment

imstuck · Answer

Solve for x using Pythagorean's Theorem, you get $$x ^{2}+(-4)^{2}=(5)^{2}$$which equals$$x ^{2}+16=25$$

imstuck · Answer

$$x ^{2}=25-16$$$$x ^{2}=9$$$$x=3$$

imstuck · Answer

And it is a positive because y is positive in Q2.  So now you have this angle with these sides:|dw:1404352583736:dw|

imstuck · Answer

Now that you have sin = 3/5, you have to find $$\sin \frac{ \theta }{ 2 }=\sin \frac{ \frac{ 3 }{ 5 } }{ 2 }$$

imstuck · Answer

$$\sin \frac{ \theta }{ 2 }=\frac{ 3 }{ 10 }$$

anonymous · Answer

Thanks i get it now!

imstuck · Answer

Half angles...poop.

anonymous · Answer

Ok so i put 3/10 in for the answer and it didnt work?

imstuck · Answer

That's because this is a half angle problem...

imstuck · Answer

Working on it now...

anonymous · Answer

OK

imstuck · Answer

I'm working it using the formula which I completely overlooked while I was typing before.  Let me get a handle on it for a sec.  I'll come up with the answer then tell you then explain it.

anonymous · Answer

Ok

imstuck · Answer

Big fat duh!  I was making this WAYYYYYYY harder than it had to be!  That's why it took me so long!  Here we go...

anonymous · Answer

ready

imstuck · Answer

Using your formula for the half angle, this is what you do:  you replace the "cos theta" with -4/5:

imstuck · Answer

$$\pm \sqrt{\frac{ 1-(\frac{ -4 }{ 5 }) }{ 2 }}$$

imstuck · Answer

Getting a common denominator we have:

imstuck · Answer

|dw:1404354222147:dw|