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Re: Why Tangent is Better than Sine and Cosine

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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 06:41 PM
My argument will show that sine (sin) and cosine (cos) are inferior to tangent (tan). These terms are on scientific calculators and are used in trigonometry. You can find angles without using a protractor, or you can find the lengths of each side of a triangle with just an angle and one side. One time, I went outside to measure a flagpole. Crazy! It would be dangerous to climb that! However, I didn't have to climb it, I stood six metres away from it and measured the angle of inclination with a clinometer. The angle (θ) was about 50°. Six metres, the ground, was the adjacent (adj). The height of the pole would be the opposite (opp). Since tanθ=opp/adj, I used that. I discovered that, after adding the altitude of the clinometer with the opp, the flagpole was 8.2 m tall.

I know all the other formulas and how to use them, but only tan could be used in this case. Why? Because it's so superior. Why would you need to find out the length of an imaginary hypotenuse (hyp)? How could one measure the opp if it was that tall off the ground? In this situation, you could only easily measure the adj. The hyp is unimportant for finding the height of something so tall. You see, you can find out the height of anything, no matter how tall, as long as your clinometer is advanced enough. Only with tan. You could measure the Eiffel Tower with tan! Just stand metres away from it and point a clinometer at the top, then use the tan formula!

Another reason why tan is so great is because 1tan^-1=45. Big deal, right? Yeah, it is. 1sin^-1=90 and 1cos^-1=0. Useless! Why? Have you ever seen an acute angle that was 90° or 0°? Don't even tell me you did. That's impossible. But an acute angle can be 45°. If θ=45° and opp=10, then tan45=10/adj, ∴ adj=1*10. So adj is 10! You didn't even have to think about that to figure it out! You can't do the same with sin or cos however. Simply because θ is acute only, never a right angle or 0°, whatever you call that. tan is nicer on high school students or math enthusiasts!

My last reason for praising tan is because it's the only one which could have answers higher than 1. Since the others have hyp as the bottom in the formula, which always has the greater value, sinθ<1 and cosθ<1. From what I know, they can't go lower than -1 either. But tan has more possibilities! Since opp can be bigger than adj or adj bigger than opp, there are infinite possibilities with tan! Well, not really, since tan brings you from -90 to +90. sin and cos limit you to -1 to +1. That's very boring, having to have only decimals. So if you use inverse sin (sin^-1) or inverse cos (sin^-1) on a number that isn't inbetween -1 and +1, you will get an error. Error! But you can inverse tan (tan^-1) on anything! tan makes no mistakes; it is flawless. Go ahead, try to find an error using only tan or inverse tan and numbers. You can't.

If you aren't aware that tan is the best by now, I pity you. It is clearly perfect as it will never lead you to a mistake, find out the height of anything possible, and it makes maths easy in solvable-without-a-calculator. Thanks for reading my persuasive essay on the importance of tangent, the superior trigonometric function. Just try to argue that tangent isn't the greatest. Again, you can't.
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Varese is not online. Varese
Joined: 01 Feb 2013
Total Posts: 1685
14 May 2013 06:46 PM
praise tangent ! :)
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 06:48 PM
*easy and solvable-without-a-calculator.

Please point out any mistakes in my essay if you see them. I'm not mistakeless like Lord tan.
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 09:13 PM
No one says anything because they can't deny He Who Makes No Mistakes (tan).
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julienmauriemort is not online. julienmauriemort
Joined: 09 May 2009
Total Posts: 21560
14 May 2013 09:13 PM
Oh god my brain hurts


I was never really on your side.
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Varese is not online. Varese
Joined: 01 Feb 2013
Total Posts: 1685
14 May 2013 09:25 PM
ot is scared of tan the superior
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 10:46 PM
Tangens est magnum.
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Hyphalax is not online. Hyphalax
Joined: 15 Jul 2011
Total Posts: 22375
14 May 2013 10:48 PM
yeah i agree tangent is the most useful

hypotenuses are a pain in the ass to work with

also this is funny because my extremely slow geometry class just started trig
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
Total Posts: 48664
14 May 2013 10:56 PM
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 11:10 PM
"what if I want to know how far away I am from the flag, or away from the top of the flag, and not the height of the flag"

You would use a tape measure on the ground, and even if you wanted to use an alternative adj, you'd have to measure the hyp or the opp...

Why would you want to measure the hyp? That's nonsense. Why would you want that? Why is it even important in any case?
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
Total Posts: 48664
14 May 2013 11:12 PM
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 11:15 PM
It's thousand times more important than the hyp. Maybe you want to make another flagpole and have it the same height as that one. Maybe you want to compare it to the height of something else.
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
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14 May 2013 11:15 PM
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Vypo is not online. Vypo
Joined: 01 Dec 2012
Total Posts: 764
14 May 2013 11:17 PM
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 11:18 PM
I do. It is important to compare it to other things, maybe you want to describe the size of something else to somebody, or maybe you want to know how much taller it is than you. Get out you blasphemer.
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 11:21 PM
Also it's impressive. You'll just take out the clinometer machine, lay measuring tape on the ground, and whip out a calculator. Then you'll tell this guy that, "The flagpole's 9 metres tall." He'll be like, "Mathematical!"
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
Total Posts: 48664
14 May 2013 11:23 PM
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
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14 May 2013 11:24 PM
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 11:28 PM
"The building is as tall as two flagpoles stacked!"
"A flagpole is so big, it's almost three times taller than me."

You would care because comparing things gives you some perspective. And it's good that your country or whoever do not know what that is. The more to amaze them with your trigonometric skills.
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
Total Posts: 48664
14 May 2013 11:32 PM
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XoboCat52 is not online. XoboCat52
Joined: 12 Apr 2013
Total Posts: 1120
14 May 2013 11:33 PM
wot m8
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 11:33 PM
Don't even tell me that you may want to measure the hyp. Why the Неll would anyone want that over the height? Don't you think the height of it is more important than an imaginary line? And don't tell me that you want to measure how far you are from it, because that would require climbing up the flagpole and then shooting the clinometer at... uh, is this possible? No I don't think you can find it this way, because you would be on top of the flagpole instead of a measurable distance away from it. You'd have to mark the ground or something and then climb.
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sinii is not online. sinii
Joined: 30 Sep 2011
Total Posts: 15218
14 May 2013 11:37 PM
"The building is as tall as two flagpoles" is a lot more informative than "the building is bigger than the flagpole." You can actually imagine the size of the building with my idea. However, if you were to say it's just bigger than the flagpole, it could be 10 metres tall or 100 metres tall. It is too vague. And 90% of your countrymen hate math because it's too smart for them. If someone's good at it then they'd think they're very intelligent. And I do care how tall a flagpole is. The people who built it cared how tall to make it.
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
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14 May 2013 11:37 PM
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extemmasfriend2 is not online. extemmasfriend2
Joined: 08 Apr 2009
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14 May 2013 11:39 PM
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