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2007
Tue
16
Oct

# “So This Is How It All Ends …”

(19)
Tuition given in the topic of A-Maths Tuition Questions from the desk of at 5:07 pm (Singapore time)

continued from the previous post.

So much for her ‘supernatural trigonometric powers’.

As the tsunami neared the beach, Miss Loi’s eyes widened as she watched, life jacket in hand (donated by Peter), it transformed into a terrifying monstrous column of water with a height so high, it approached infinitely into the sky.

“So this isn’t a cosine wave, but a powerful tangent wave … and this is how it all ends.“, thought Miss Loi as she stood and closed her eyes, bracing herself for the inevitable.

At that very moment, a familiar Darth Vader-ish voice echoed in her head …

Despair not, my sexy young tutor, for I have the power to save thee!

… and that jolted Miss Loi out of her self-induced trance.

For thy contribution in helping generations of slackers in Mathematics, I shall part the sea for thy safe passage.

But alas in order to do that, thou must supply Me the amplitude, and period of the tsunami, and by how much it has shifted along its vertical axis, for My mathematics is not as good as thine.

Seconds now remained before the waves hit the shore, and Miss Loi barely had enough time to produce the amended equation of this killer wave:

The diagram shows part of the graph of y = atan(bx) + c. Find the values of a, b and c.

Note: A sudden hunch led to Miss Loi including this tangent graph question, as after lying dormant for a long time, the powerful tangent tsunami had finally made its first appearance in June 2007 (this year).

### Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

1. Peter commented in tuition class

2007
Oct
17
Wed
12:21am

1

Peter shouts - "Stop holding the life jacket and wear it!"

and keeps running 🙂

2. ByPassing commented in tuition class

2007
Oct
17
Wed
9:07am

2

Wah~duck vendor leh~....This post trigger my force-sensitive midi chlorian bacteria...i dont think Vader will react that way.

In fact, first you will hear this from him

Then he might say this to you for the lack of faith

Lastly, for giving up so easily, might provoke him in saying this

P.S Miss Loi...you sure u not a Master Jedi of corkster+lamer..hehe

3. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
17
Wed
9:29am

3

Peter, Miss Loi's too stunned in awe of the tangent wave to hear your plea. Only the values of a, b and c can save her now!

4. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
17
Wed
1:39pm

4

Hey Bypasser,

Miss Loi can hear only 1 of the 3 voices of your Duck Vendor, so she concludes that this Duck Vendor's a fake!

P.S. Your long, long hyperlinks to Duck Vendor's 'voices' have created some alignment problem on the comments area, so they've condensed (sort of).

5. HORNY ANG MOH commented in tuition class

2007
Oct
17
Wed
4:37pm

5

I don't care what sort of wave cum crashing down!!!!! If I see a se*xy math teacher sure I will rush in to save u wan!!! And they both lieve happly after that!!! He! He! Have a nice day!

6. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
17
Wed
10:35pm

6

Oh that's so touching and heroic of you, HAM. But if Miss Loi's an ugly old lady then it'll be a completely different deal right? Men ... tsk!

7. ByPassing commented in tuition class

2007
Oct
17
Wed
11:41pm

7

oops...didnt meant to cause any alignment problem...so sorry.

well, actually the first link should be this

Back to how it all ends, if its inevitable that i cant escape, i think i might just stand there and let myself be consume by the tsunami.

8. Peter commented in tuition class

2007
Oct
18
Thu
3:59am

8

Heeyyyy don't lump all men together! I *DID* give you a life jacket, and it's not because you're a sexy maths 'cher.... :p

9. kiroii commented in tuition class

2007
Oct
18
Thu
4:00am

9

c=3

Yes you got this right. As you know,

tan 0 = 0 (regardless of what a is) but the graph indicates 3
⇒ graph is shifted upwards by 3
c = 3

a=1

Sadly this is where students get caught out by the tsunami. The amplitude of your regular tangent curve is 1 and this occurs at every odd multiple of π/4 (45o) i.e. ±π/4, ±3π/4.

Look at the graph again dude. It's been specifically indicated there that y = 5 when x = π/4, and y = 1 when x = -π/4.

Taking one of these points and sub in the values of b and c, you'll get

atan(π/4) + 3 = 5
a = 2

b=1

Yes this part looks like your regular tan curve indeed. The standard period of a tangent graph is π(180o) with tan x approaching infinity at every odd multiple of π/2 (90o) i.e. ±π/2, ±3π/2 ... As the graph is consistent with these properties, the period is still π and hence b = 1.

i dun see how to a and b values could differ since its the same as a regular tan curve

correcto?

btw ya mean tan may actually appear? for the last 10years it has never appeared-.- i nv even study tan>.

10. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
18
Thu
2:20pm

10

I know I suck in Mathematics but do not idle and stand there and underestimate the power of Mathematics!

Quick! Give Me the values of a,b & c so that I can save my sexy young tutor!

11. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
18
Thu
2:23pm

11

Peter, instead of running off like that, ever considered carrying Miss Loi to safety?

But that'll be another maths problem to calculate her weight. LOL

12. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
18
Thu
2:27pm

12

Ahhhh finally Kiroii the hero to the rescue!

And so legend has it that a brave martyr got swept away by the tsunami in his quest to save the poor damsel, all because he miscalculated its amplitude (see comments in your workings)!

P.S. Hope this will refresh your knowledge of tangent curves 😉

13. kiroii commented in tuition class

2007
Oct
19
Fri
7:17am

13

erm miss loi i dont quite get what ya mean by amp..my textook doesnt have amp wad de>.

14. Peter commented in tuition class

2007
Oct
19
Fri
9:39am

14

I *did* consider carrying you off into the sunset....

But then you wouldn't be able to make up maths problems from your predicaments heheheh!

15. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
19
Fri
11:09am

15

Kiroii, okay strictly speaking the tangent graph does not have an 'amplitude', as you can see, it stretches to ±∞.

However the coefficient a represents how far vertically the graph is stretched, and this can be calculated as described previously. And in trying to be analogous to the sine and cosine graphs, Miss Loi refers to this as the 'amplitude' of the tangent graph. But maybe she should stop doing that to avoid confusion 😛

16. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
19
Fri
11:13am

16

Peter, what makes you think Miss Loi can't make up maths problems from the predicament of being carried by you? Should be interest ... maybe some formula regarding her weight hahaha.

17. Peter commented in tuition class

2007
Oct
19
Fri
1:30pm

17

Sexy Maths 'Cher... welllllll since you put it that way, I'll have to swoop by you in your following episode and carry you off while you're trying to figure out the log tables 🙂

(again I stress, I suck at maths... to me a log is a piece of wood, or in context of computers, a record of events that happened in the server hehehe!)

18. ByPassing commented in tuition class

2007
Oct
21
Sun
12:53am

18

haha....the value of a, b and c?... u take knife stab me ba

19. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2007
Oct
21
Sun
1:54pm

19

Peter, Miss Loi did refer to the log as a piece of wood what! 😛

Bypasser, for your utter lack of chivalry, you've just been stabbed *twists knife*!