Question

is this undefined??

sec(arcsec1/2)

undefined
-1/2
1/2
2

Answer 1

@superdavesuper could you help me with this question also??(:

Answer 2

it is the sec of the angle whose sec is 0.5

Answer 3

@douglaswinslowcooper which would be 1/2 correct?

Answer 4

Just so.

Answer 5

but then since sec=1/cos; which means cos=2....so it is undefined :)

Answer 6

@superdavesuper right?? so it is undefined!

Answer 7

well @douglaswinslowcooper eqn is right as well....but....im sticking w my ans though lol

Answer 8

Good point, cannot have sec = 1/2 as cannot have cos = 2. My error.

Answer 9

Guys, remember that the secant and inverse secant functions "undo" each other.

Thus, sec(arcsec 1/2)=1/2.

Answer 10

woah then its not undefined...? im confused ):

Answer 11

@mathmale but u evaluate the expression from the innermost bracket first, so i think it would become undefined BEFORE it got "undo" by the outer sec function. Just my opinion thou...

Answer 12

okay! sorry for asking but would it be 30 degrees if i simplify arccot sq.root3/3?

Answer 13

@ttop0816 u may want to ask 4 more opinions on ur original prob.

as for arccot(sqrt(3)/3)...
let it be x, so cotx=sqrt3/3, so tanx=3/sqrt3
x=60

Answer 14

I am with mathmale, sec ( arcsec (something) ) = something.

Answer 15

Don't tell me I was wrong about my being wrong!

Answer 16

ohhhh then it is 1/2?

Answer 17

Yes.

Answer 18

http://www.wolframalpha.com/input/?i=sec%28arcsec+%281%2F2%29%29%3D

Answer 19

alright i will do a shout-out...
@satellite73 @Hero @ganeshie8 @RadEn should the expression sec(arcsec1/2) be undefined or 1/2? thanx for ur hlep! :)

Answer 20

Let me help @ybarrap @whpalmer4 @wolfe8

Answer 21

I was abused on a Mathematics section when someone came and asked for stories about abuse....

Answer 22

good one @douglaswinslowcooper

Answer 23

@GymnasticsGirl9052 there is no need to post ur question within someone else's. plz go post it as ur own. thank you :)

Answer 24

Just kidding around, GG.

Answer 25

Would someone please look up the graph of the secant function? If so, it'll become evident that the secant is always >= 1 or <=-1. Therefore, the correct answer to the problem posted by @ttop0816 is "undefined." My initial response (1/2) was wrong, and I apologize.

Answer 26

I don't agree!! they ask for the sec (arcsec (1/2) ) not sec (1/2)
If you say so, so wolfram's answer is wrong???

Answer 27

f[undefined] = undefined, I think.

Answer 28

Can anyone come up with an angle whose secant is 1/2?
Note that this question is equivalent to asking:
Can anyone come up with an angle whose cosine is 2/1?

Answer 29

hmmm... sec(arcsec(1/2))
let arcsec(1/2) is theta.
if we draw it, looks the hypotenuse smallest then the leg of triangle. while in right triangle the hypotenuse always be longer, right ?

Answer 30

RadEn...please come to a conclusion and share it with the rest of us.

Answer 31

wish OS has a way to post a poll - it would be perfect for a question like this :)

Answer 32

i want represented it in a diagram, but tool draw is not working now.
to me, it is not exist. haha :P

Answer 33

Or, paraphrased, there is no angle whose secant is (1/2).

Would someone care to evaluate arcsec 2?

Answer 34

one more round n i will call it quit on this...
@jim_thompson5910 @agent0smith should the expression sec(arcsec1/2) be undefined or 1/2? thanx for ur hlep! :)

Answer 35

Undefined. arcsec(1/2) does not exist.

Answer 36

Yeah, the domain of arcsec is as stated above, x<-1 or x>1

Answer 37

thank you @ranga! kind of disappointed that wolfram didnt check for bound in its calculation.

Answer 38

thank you @agent0smith

Answer 39

Thank you all....sorry i already gave out the medal on this earlier but u have my eternal thanks! :)

Answer 40

You can only "cancel out" the sec(arcsec ...) IF the ... is in the domain of the inner function.

More simple example: cos(arccos 2) cannot equal 2, right? cos(...) can't be >1

Answer 41

But even still... http://www.wolframalpha.com/input/?i=cos%28arccos2%29

Answer 42

:( wonder if we can report that to wolfram! lol

Answer 43

^i think it's because they do it over complex numbers, so... http://www.wolframalpha.com/input/?i=arccos2

Answer 44

damn....i must have slept thro THAT part of my trig class!!! O^O thanks again @agent0smith

Answer 45

^no, i've never learned complex solutions to inverse trig functions either

Answer 46

Yes, that's correct — ArcSec of a complex number...

See http://mathworld.wolfram.com/InverseSecant.html

Answer 47

I'm happy to say that I've avoided needing to know that stuff for more than 50 years, and hope to keep it that way for another 50 :-)

Answer 48

but yes, a very interesting thing to figure out!

Answer 49

hmmm.....thanks i guess @whpalmer4 lol

so based on the wolfram description: if "Arcsecz being used for the multivalued function" then i guess the answer would be 1/2; but it is referring to the principal value only, then it would be undefined....

OK this is it.....i guess everyone is right then :)

Answer 50

@superdavesuper yep and it's very likely this is from a standard precalc/trig class, one that would not deal with complex number solutions

Answer 51

we were more arguing on principle than anything else as we dont expect the "textbook" solution would come anywhere close to what are being discussed here :)

Answer 52

@superdavesuper 100% agree!! I was taught that a *b =0 --> a =0 or b =0
now I am taught that a*b =0 and no need to have either a =0 or b =0 (in other word a !=0 and b!=0)

Answer 53

hi5 @Loser66 :)

OK everybody goes home happy! lol im out of here - again thank you all for ur contribution!!

Answer 54

let's just hope that no one had the misfortune of answering -1/2 or 2, no amount of "math lawyering" is going to get you a correct mark there :-)