Some silly Question

[Aqualim]

Just looking back over the Year 11 book to see if there was anything i didn't know how to do and stumbled along this:

Find the acute angle between the lines with equations and

[Ilovemathsmeth]

Find the gradient of each line; that is, 2 and -4 respectively.

Keep your calc in degree mode.

Find tan inverse (2) = 63.43494882 deg.
Find tan inverse (-4) = -75.96375653; add 180 to give 104.0362435 deg.

The rule theta 2 -theta 1 gives interior angle; i.e. larger angle - smaller angle.

Answer should be 104.0362435 - 63.43494882 = 40.60129465

Watch out if it asks 'obtuse angle' - you'd need to subtract above angle from 180 if so.

Hope that helps.

[Ilovemathsmeth]

The reason why you add 180 above is because you want to find the angle each line makes with the positive direction of the x-axis. In the above, the neg result is not in the pos direction.

[Aqualim]

Cheers thanks for that, I was thinking something along the line.. So when you sketching it, how do you know which part you are look for, as in which part of the graph are you looking for the distance between

[qshyrn]

heres how i did it (look at attachment) hope u understand
EDIT:  umm u dont really need to find out which one is the obtuse/acute at first, just find one of the angles between the lines then u can find out the other one and therefore know which one is obtuse and acute

[/0]

Another way for people doing spesh is to turn them into vectors:

A vector representing is

A vector representing is

Thus, by the dot product, we have



So the angle between the vectors is , and the acute angle is

[crappy]

Another way for people doing spesh is to turn them into vectors:

A vector representing is

A vector representing is

Thus, by the dot product, we have



So the angle between the vectors is , and the acute angle is

gotta love spesh lol

[/0]

haha yeah I never got the hang of angles between lines. I trust vectors though

[Aqualim]

So basically in a nutshell, if they ask you to find the Acute angle, you add 180 (to ensure that the figure is a positive number), but for obtuse you would subtract 180 make the figure negative??

[Ilovemathsmeth]

Amazing, /0, you turned those lines into vectors so quickly! Are vectors hard in Spesh?

[Hooligan]

Amazing, /0, you turned those lines into vectors so quickly! Are vectors hard in Spesh?

Nahhh... vectors aren't too hard. xD You aced Methods, so I'm pretty sure you wouldn't find Spesh too hard.

[Hooligan]

Another way for people doing spesh is to turn them into vectors:

A vector representing is

A vector representing is

Thus, by the dot product, we have



So the angle between the vectors is , and the acute angle is

Hey /0, can you show me how you converted those linear equations into vector form? I'm interested... I never recall converting linear to vector in Spesh...

[/0]

I just picked vectors that had the same 'gradient' as the lines.
Since the location of the vector isn't important, I ignored the and translations.

Instead I had and

Since the coefficient of gives the 'rise' and the coefficient of gives the 'run',

You can say

And then sub in

[Ilovemathsmeth]

Vectors sound exciting but a little scary, so many weird lines in the Spesh book

Thanks Hooligan I'm so lazy, I'll have to start it soon but I've got ages, especially if I take Gap year.

[Hooligan]

I just picked vectors that had the same 'gradient' as the lines.
Since the location of the vector isn't important, I ignored the and translations.

Instead I had and

Since the coefficient of gives the 'rise' and the coefficient of gives the 'run',

You can say

And then sub in

How interesting! ^_^ Thanks /0!! I have never used Vectors in this sort of setting.