Question

True or false?

Answer 1

True for 17 and 18, right?

Answer 2

Yes, as \[\csc^{-1}(\csc)\] and \[\sec(\sec^{-1})\] cancel each other out

Answer 3

@Astrophysics but there is restrictions on their domains to cancel each other out.

Answer 4

What kind of restrictions?

Answer 5

Yes, that's true and rather then writing it all out you can check this out: http://users.math.msu.edu/users/gnagy/teaching/12-spring/mth133/l11-133.pdf

Answer 6

But both of these questions would be true... correct?

Answer 7

Do you understand why they are true though? :)
Like.. do you understand why this one would be false?\[\large\rm \arccos\left[\cos\left(-\frac{\pi}{3}\right)\right]=-\frac{\pi}{3}\]

Answer 8

Zep, the equation is not showing up :/

Answer 9

Refresh page maybe? :O

Answer 10

Oh, better!
Okay... so that one would be false? Why? Because it's not part of the restricted function of cosine?

Answer 11

Yessss. Inverse cosine must spit out an angle in Q1 or Q2, right?

Answer 12

So I think... I think...
with these composition problems,
you only need to be careful...
when the inverse function is on the outside.

When it's on the inside, it should always work out to be true...
I think...

Answer 13

^that's not true (for cancellation purposes)

Answer 14

Right right.
Hmmm. I'll keep an eye out. thanks for the heads up!

Answer 15

Yeah, so both of yours would be true

Answer 16

what's not true?

Answer 17

@Abbles my reply was to @zepdrix \[\large \cos ( \arccos 2) \] for example. They're just easier to spit.

Answer 18

*spot...

Answer 19

Oh true, they might give you some goofy shinanigans like that.

Answer 20

You crack me up xD

So agent, cos(arccos2) would be undefined?

Answer 21

Yes, since the domain of arccos is [-1, 1]

Just like the domain of cos is [0, pi] (for inverse cosine purposes)

but... \[\large \arccos (\cos \frac{ 7\pi }{ 4 })\]is still defined. It is just equal to 7pi/4.

Answer 22

Wait, how is that last example still defined? If 7pi/4 is greater than pi?

Answer 23

Dammit. It is just NOT equal to 7pi/4.

Answer 24

The last is still defined, because find the value of cos 7pi/4, THEN find the arccos of that value.

Answer 25

XD

Answer 26

\[\large \cos \frac{ 7\pi }{ 4 }= \cos \frac{ \pi }{ 4 }\](look at a unit circle to see why)

Thus, \[\large \arccos (\cos \frac{ 7\pi }{ 4 }) = \arccos (\cos \frac{ \pi }{ 4 }) = ?\]

Answer 27

Aha! I see what you're saying :) Lol.
Thanks for explaining that!

Answer 28

That sounds like a delicious poker hand.
"I've got a full house, pi's over fours."

Answer 29

Sorry... sometimes I make sense...
and sometimes... -_-

Answer 30

Similarly, \[\large \arccos ( \cos \frac{ 7\pi }{ 6 }) = \arccos (\cos \frac{ 5\pi }{ 6 }) = ?\]Again see a unit circle to see why you can do that with the angles

Answer 31

@zepdrix ha, I used to play poker for a living.

Answer 32

Rolling on the floor.
Laughing.
For real.

Answer 33

Rolling on the floor.
Laughing.
A DELICIOUS poker hand omg hahaha.

Answer 34

haha XD

Answer 35

Ya I had pie* on the brain.
So the pi didn't make a lot of sense.
Honestly, none of that sentence made sense though lol

Answer 36

@agent0smith ooo nice :D

I did pretty well for a couple years myself.
Not enough to live off of though XD haha

Answer 37

You have pie on your brain?
Makes sense... xD

Answer 38

Heyy Agent played poker, eh? Somehow that fits the image I had of you in my mind... serious... poker face... yeah

Answer 39

Speaking of pie on the brain,
I remember memorizing like 200 digits of pi for a school contest back in the day :) that was kinda fun lol

forgotten all of it by now though XD

Answer 40

:O

Answer 41

Really? I would have imagined MI6 or something.
Secret aaaagent man!

Answer 42

Haha

Answer 43

Haha, yep. It was my sole income for about four years. Not a great soul income, however.

Answer 44

Wow, impressive. And haha xD nice one.

Answer 45

Zep, you had so much pie in your brain, it pushed everything else out.

Answer 46

4 years... that's crazy. You must be one heck of a poker player.

Answer 47

I'd say I'm pretty good. I don't play much seriously anymore, but I'm still pretty sharp. A few days ago I tutored a guy for a few hours, and that was fun - being paid to talk about poker.

Answer 48

That's awesome. Why'd you stop after four years?

Answer 49

If I ever decide to pick up poker as a hobby, I'll hit you up.

Answer 50

US government decided to intervene with online poker, and, as they are wont to do, ruined things.

Sure, I can give you an OS discount haha. I used to tutor poker friends on skype for free, but that's cos we'd be somewhat mutually helping each other learn/improve.

I was teaching people about poker, before I was teaching anyone math/physics.

Answer 51

//\\ I'm a witness^^

Answer 52

Oooh. I see. The government is out of control. That's why I moved to Chile. Hah.

OS discount? Awesome! Maybe when I'm not so swamped with school work, I'll hit you up on that offer.

Answer 53

@YanaSidlinskiy witness to what?

I know a few poker players who did the same (moved to Canada, Costa Rica, et al., to continue playing poker online).

And sure :)

Answer 54

Costa Rica's a good one. Never heard of people moving to play poker online though! That's hilarious.

Answer 55

Well, some of the guys I knew made a lot of money, and they didn't want to give that up. And they were mostly young, single guys, so why not haha.

Answer 56

Ha! Very true. Might as well travel while you still can without worry about responsibilities and such.