cosine question (1 Viewer)

[frenzal_dude]

hey hows it

cosx = 2 +/1 sqrt6

if -180 is lessthan or same as x, which is lessthan or same as 180, find x.

the answers say its +/-116 degrees 43 minutes, but when i shift cos 2 +/1 sqrt6
it comes up as an error!?

 

[Dreamerish*~]

hey hows it

cosx = 2 +/1 sqrt6

if -180 is lessthan or same as x, which is lessthan or same as 180, find x.

the answers say its +/-116 degrees 43 minutes, but when i shift cos 2 +/1 sqrt6
it comes up as an error!?

What is "+/"? It can't be "square root" because you have that as "sqrt".

It might help if you wrote your question and scanned it, or just draw it up in paint.

 

[frenzal_dude]

haha sorry mate, i meant +/-

So the question is cosx = 2 +/- sqrt6

ie. cos x = 2 plus or minus the square root of 6

 

[Dreamerish*~]

haha sorry mate, i meant +/-

So the question is cosx = 2 +/- sqrt6

ie. cos x = 2 times the square root of 6

So... +/- means "times"?

cosx = 2√6, -180° < x < 180°

It comes up as an error because 2√6 does not lie between -1 and 1. Are you sure you copied the question correctly?

 

[frenzal_dude]

lol sorry mate i stuffed up again, im heaps tired sorry. ok this is the actual proper question:

cos x, equals two plus or minus the square root of 6

 

[Dreamerish*~]

lol sorry mate i stuffed up again, im heaps tired sorry. ok this is the actual proper question:

cos x, equals two plus or minus the square root of 6

Haha, ok then.

cosx = 2 + √6

It can't be 2 + √6 because that does not lie between -1 and 1, and would have no solution for cosx.

So the question is cosx = 2 - √6, for -180° < x < 180°

cosx = -0.449489742

x = cos^-1(-0.449489742)

x = 116° 42', -116° 42'

 

[Shael]

Just wondering Dreamerish, in your sig.. is that the guy from "House"?

 

[Dreamerish*~]

Just wondering Dreamerish, in your sig.. is that the guy from "House"?

Correct!

It's Hugh Laurie, possibly the most amazing old man I've seen.

 

[Shael]

Hehe awesome. Did you draw that?

EDIT: nvm.. I see the "Gary" signature.

 

[frenzal_dude]

k so its 116`42, but where does the -116`42 come in? and what exactly does it mean that its between -180 and 180, does this have soemthign to do with astc?

 

[Dreamerish*~]

k so its 116`42, but where does the -116`42 come in? and what exactly does it mean that its between -180 and 180, does this have soemthign to do with astc?

-180° < x < 180° simply means x lies between -180° and 180°.

Yes, it has to do with ASTC. Your answer would normally be just 116° 42' if it was for x < 180°, but since it's extended to -180°, you need to take into account values for x which are below zero.

From the previous post, you saw that cosx = -0.449489742, which is negative.

cos is negative in the second and third quadrants. 116° 42' lies in the second quadrant if you go anticlockwise - ASTC. However, you can also go clockwise up to -180° in this question, so if you go clockwise, your answer would be 0 - 116° 42' = -116° 42', which likes in the third quadrant, and will still give you a negative answer for cosx.

I'm sorry for explaining it in such a crap way. How about I attach a graph?

 

[frenzal_dude]

ok i think i would be able to do this question fine if it wasnt for the x is between -180 and 180, because i know that cos is negative in S and T quadrants, and i know how to find them, but i still dont get teh -180 part, if htey want both answers would it just be x is between 0 and 360?

 

[frenzal_dude]

ahh i think i get it now! its not x is between 0 and 360 because otherwise the answer would be 116`42 and 243`42, but because x is between -180 and 180, u go from 0 backwards, so its 0 - 116`42 which is hte 2nd answer!

is that right?

also thanks so much for your help, thanx for doing that diagram that helped explain it alot 2!

 

[Dreamerish*~]

ahh i think i get it now! its not x is between 0 and 360 because otherwise the answer would be 116`42 and 243`42, but because x is between -180 and 180, u go from 0 backwards, so its 0 - 116`42 which is hte 2nd answer!

is that right?

also thanks so much for your help, thanx for doing that diagram that helped explain it alot 2!

Correct! Well done.

You're very welcome.