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.

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).

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!

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 (45^{o}) 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(180^{o}) with tan x approaching infinity at every odd multiple of π/2 (90^{o}) 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>.

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 😉

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 😛

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.

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!)

* Please refer to the relevant Ten-Year Series for the questions of these suggested solutions.

About Miss Loi

Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths tuition. Her life’s calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over years she has been a savior to countless students … [read more]

Gratitudes

Ever since I started attending Joss Sticks, algebra and everything else seems so much easier! Everyone was pretty shocked when they found out I got an A1 for both A-Math and E-Math … [read more]

## 19 Comments

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

and keeps running 🙂

曜

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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

曜

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Peter, Miss Loi's too stunned in awe of the tangent wave to hear your plea. Only the values of

a,bandccan save her now!曜

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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).

曜

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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!

曜

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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!

曜

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

well, actually the first link should be this

Second link should be this

Since 3rd link worked.

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.

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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

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c=3

Yes you got this right. As you know,

tan 0 = 0 (regardless of what

ais) but the graph indicates 3⇒ graph is shifted

upwardsby 3⇒

c= 3a=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 (45^{o}) i.e. ±π/4, ±3π/4.Look at the graph again dude. It's been specifically indicated there that

y= 5 whenx=π/4, andy= 1 whenx= -π/4.Taking one of these points and sub in the values of

bandc, you'll getatan(π/4) + 3 = 5⇒

a= 2b=1

Yes this part looks like your regular tan curve indeed. The standard period of a tangent graph is

π(180^{o}) with tanxapproaching infinity at every odd multiple ofπ/2 (90^{o}) i.e. ±π/2, ±3π/2 ... As the graph is consistent with these properties, the period is stillπand henceb= 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>.

曜

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Darth Vader-ish voice to

Bypasser:曜

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Peter, instead of running off like that, ever considered

carryingMiss Loi to safety?But that'll be another maths problem to calculate her weight. LOL

曜

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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 😉

曜

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

曜

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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!

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

However the coefficient

arepresents 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 😛曜

日

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.曜

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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!)

曜

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

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Peter, Miss Loididrefer to the log as a piece of wood what! 😛Bypasser, for your utter lack of chivalry, you've just been stabbed *twists knife*!