Can you see what the problem is? If sin(theta)=1/2 and cos(theta)=3/4, then tan(theta)=?

If sin(theta)=1/2 and cos(theta)=3/4, then what's the value of tan(theta)? I almost put this question on a test for my trig students but lucky I caught a mistake in the problem before I do so. Can you see the problem in the problem?
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#math #algebra #mathbasics

[@bprpmathbasics]

Hate to be that guy but I need the extra credit: kzbin.info/www/bejne/qZaTd3x5gJtppck

[@Steve_Stowers]

Logically, when P is a false statement, "If P then Q" is true for any Q. So any answer to that question should be considered correct.

[@danielnoe5782]

I agree. It’s the same reasoning for this statement being true “if the moon is cheese, then I can fly.” Assume the moon is cheese. Thus, I can fly.

[@xinpingdonohoe3978]

Indeed. There are three ways to logically conclude things. T→T, F→F, F→T. This starts with an F, so we can get anything we want, whether T or F (though I don't know if any single answer counts as true within this context).

[@stephenbeck7222]

But here tan theta depends on theta itself, and there is no value of theta that makes sense in the problem so there is no definition for tan theta. It’s like saying, if x = x+1, then what is x^2? You can’t just declare the statement is vacuous and x^2 equals whatever you want.

[@danielnoe5782]

@@stephenbeck7222 but by the rules of logic, you can.

[@xinpingdonohoe3978]

@@stephenbeck7222 yes you can. If x=x+1, then subtract x on both sides to get 0=1. From there, multiply both sides by x²-α to get 0=x²-α. Finally, x²=α. Choose whichever α you like to let x² be whatever you want.

[@fahrrad67]

This begs for a new geometry to be described in which sin θ = 1/2 and cos θ = 3/4 can actually occur, it will be named bprp space.

[@TheWeeb-j5g]

Dude that's so normal in maths lol

[@TheWeeb-j5g]

If something doesn't exist then just make it exist lol

[@futilitariano]

Perhaps that is the sort of idea behind 2 + 2 = 5. One can show this mathematically as follows. 1. Let a = b. 2. Then ab = b^2 [multiply both sides of equation in 1. by b.] 3. and ab - a^2 = b^2 - a^2 [subtract both sides of equation in 2. by a^2] 4. Then a(b - a) = (b + a)(b - a) [factor both sides of equation in 3.] 5. and a = b + a [divide both sides of equation in 4. by b - a] 6. Since a = b [given equation in 1.], a = a + a or a = 2a 7. and 1 = 2 [divide both sides of equation in 6. by a] 8. It follows that 2 + 2 = 2 + 1 + 1 = 2 + 1 + 2 = 5. That is, 2 + 2 = 5. [ 2 = 1 + 1, 1 = 2 from equation in line 7., substitution and arithmetic]

[@genio2509]

​@@futilitarianoNo, this is different. This joke proof is actually just completely invalid as you are dividing by 0. x/0 just has no determined value, as sometimes it is 1, sometimes 0, sometimes ∞ and sometimes -∞, and that just proves you can't divide by 0. A closer example would be a riddle I've been told: A hunter is tracking a bear, he sees footprints and follows 1km south, then 1km east, them 1km north, and realizes he's in the same place. What's the color of the bear? (I'll give you space if you want to solve it lol) White because of spherical geometry, he's at the north pole. You can get a 270° triangle, and yuo can also get paralel lines that meet, and so much more.

[@richardhole8429]

I caught the errant question immediatly. SinX=1/2, X=30° Cos30° does not equal 3/4 so reject the problem. The answer is: the question is faulty

[@PlanesAndGames732]

Maybe the mistake was a square missing in the cosine...

[@ingiford175]

One thing, if you are creating a question like this and want all integers, just use a pythagorean triple. Example 3/5 and 4/5 or if want larger numbers use 5/13 and 12/13.

[@MrH4nky]

I think someone just lost a square root for the cos. Then it does make sense (sqrt(3/4) = sqrt(3)/2)

[@MadaraUchihaSecondRikudo]

Just from the thumbnail if sin(theta) = 1/2 then theta = 30 deg + 360n deg, none of the possible values of theta produce 3/4 for cos (theta), cos30 = sqrt(3)/2

[@SimsHacks]

you forgot θ = 150° + n*360°, it doesn't change anything but still

[@DrFunkman]

“…and so, you get no solution” *Me, who got 2 as their answer* : Well duh, of course there’s no solution

[@m.h.6470]

If you give these three equations to wolfram alpha with the "system of 3 equations" function: sinx = 1/2 cosx = 3/4 tanx = y it returns "no solutions exist".

[@ACertainMan]

Because there is no solution.

[@m.h.6470]

@@ACertainMan Obviously... I never said otherwise.

[@ACertainMan]

@@m.h.6470 lol

[@mgmartin51]

The question was "If...", so the answer is 2/3. Of course, there is no sin x = 1/2 and cos x = 3/4 in this universe, to the answer is "non sequitur".

[@orngng]

Vacuously true statement

[@aliskprado]

I was thinking in this line too.

[@OverclockingCowboy]

You have 2 tangent values. One for sin A = 1/2 and the other for cos B = 3/4.

[@Firor0]

Welp i hope i get this on the test

[@noahblack914]

Immediately knew something was up. Thanks unit circle!

[@davidmiedema2950]

Put it on the test as is... then extra credit for the students who recognize the error...

[@jmr5125]

I'd just put it on as a clearly marked "extra credit" question. Perhaps even with a "Yes, this is extra credit -- this question is harder than you think!"

[@ronaldking1054]

The person could invert the cos x so that it was ((4/3)^2 - 1)^(1/2) = (7/9)^(1/2) = (7)^(1/2) / 3, which does not equal 2/3. That is using the secant identity rather than the definition of tangent.

[@neilmccafferty5886]

Sin^2 + cos^2 = 13/16. Therefor cannot be a right angled triangle.

[@Chris-hf2sl]

No need to watch the video. We know that sin(x)^2 + cos(x)^2 = 1. Put the values in: (1/2)^2 + (3/4)^2 does not equal 1. Therefore the starting premises are inconsistent.

[@rodrigoqteixeira]

When I saw the thumb nail, I went to check the unit circle thingy (cos² + sin² = 1), and the radius squared of that unit circle is 0.8125 💀

[@DhoklaAboveVadapav]

Simple. sin^2(theta) = 1/4 cos^2(theta) = 9/16 sin^2(theta) + cos^2(theta) = 1/4 + 9/16 = 13/16 ≠ 1 So statement is false. Edit: I am a genius

[@futilitariano]

Since(1/2)^2 + (3/4)^2 does not equal 1, theta can't represent a single number. Recall that sin^2(@) + cos^2(@) = 1 for all real numbers @.

[@joeschmo622]

Yeh, I saw that immediately. No way sin and cos are both "clean" fractions like that. One might be, but the other would be some radical. Quick check with sin^2+cos^2=1, and nope. Only 0/+1/-1 work out cleanly.

[@jimwinchester339]

Or, you could just reason, "well, *IF* that's true, then tan(theta)=2/3; but it's not - - but IF IT WERE, that'd be true."

[@adamrussell658]

You have two different thetas. Arcsin 0.5 = 30 degrees and arccos 0.75 = approx 41 degrees

[@RealQinnMalloryu4]

sin0=(1/2)^2 cos0=(3/4)^2= {sin01/4 ➖ cos09/16}=sin0cos08/12 =sin0cos08/3^4 sin0cos02^3/3^4 sin0cos01^1^1/3^2^2 sin0cos01/3^1^2 sinocos0/3^2 (sin0cos0 ➖ 3sin0cos0+2)

[@officialkivoc]

i was thinking about how sin30 should equal 1/2, and how cos30 is definitely not 3/4...

[@Shaia_TeamLCE]

I’m guessing before I watch the video than tan = 2/3 Edit: My answer was shut down in the first 30 seconds 😞

[@franciscoGENIO13]

This is Impossible. Notice that sin²θ + cos²θ = ¼ + 9/16 = 13/16 ≠ 1

[@ChandrasegaranNarasimhan]

The triangle may not be right angled. But, I agree that the person who noticed the flaw is smart.

[@jackkalver4644]

I didn’t even have to click the video to realize that sin^2 θ +cos^2 θ ≠1

[@jacobgoldman5780]

The question is wrong but if A and B then if one is false we can give any correct answer.

[@roger9552]

The problem is sin^2 theta + cos^2 theta doesn’t equal 1

[@goyo9992]

El problema de este problema es que el planteamiento es falso: sen^2 (x) + cos^2 (x) no es 1

[@joansoldevilacaba4138]

could be possible that the person who had proposed this problem forgot the square for cosinus?

[@als2cents679]

Well, it depends on what is the value of x^2 + x when x = 1 and x^2 = 2

[@guntramschlemminger7383]

Is sin( theta ) = 0.5 the cos of the same angle can not be equal 0.75.

[@VladimírBordováč]

The problem has no solution even in complex numbers.

[@drazenbicanic3590]

If sine is equal to 1/2, cosine cannot be 3/4

[@xia-bi-ding.]

tan 0 =2/3 （不懂怎么写tan后面的😢）

[@andreykarbinovskiy430]

sin squared plus cos squared is not equal to 1

[@KKT-k2r]

the angle must be differ

[@petohunor6737]

sin(30°) =1/2 cos(30°)=sqrt(3)/2

[@joe_z]

I was trying to figure out whether you were thinking of some weird complex number, or actually meant to write cos² instead of cos (in which case it's actually fine). Turns out, nope, you just chose two wrong numbers :(

[@dlevi67]

If sin(θ) = 1/2 and cos(θ) = 3/4, then θ is the famous Heisenberg angle. Or maybe not even that, since unitarity is not maintained.

[@maxhagenauer24]

I could tell it wouldn't make sense because I was trying to make a 3-4-5 right triangle or some sort of perfect right triangle out of it with the pythagorean triples. The 1/2 and 3/4 are just the ratios and no the actual side lengths of the triangles but there would be no triangle to make that true sense they have an even denominator (2 and 4) when no pythagorean triple has an even hypotheses.

[@senhueichen3062]

5/6.

[@arpitpatel5814]

My friend, There exist NO θ which satisfy your question There exist no θ which satisfies If Cos(θ) = 1/2 Then Sin(θ) = 0.866 It cannot be 3/4 Your θs in sin and cos are different This is basic mathematics You cannot use θ in both terms Keep trying, Maths is beautiful.❤

[@david_porthouse]

Brown

[@cyrusyeung8096]

Usually, either sin(theta) or cos(theta) is given, and students are required to find the other one.

[@IloveRumania]

tan(theta) = 2/3

[@JJ_TheGreat]

2/3

[@dannyyeung8237]

Is sin²θ+cos²θ=1 true for all complex values θ as well? By the way if θ is a complex number, it is equal to a+bi for some real number a and b and i=√(-1)

[@dabs4270]

yes, sin²θ+cos²θ=1 is true for all θ, including complex numbers

[@Musterkartoffel]

1:40

[@xinpingdonohoe3978]

Yes, it's true for all numbers. And it's generally agreed that it's better to say i²=-1 rather than i=√(-1).

[@user62490]

That's not even a triangle for all possible values

[@carultch]

It's not even possible with complex values of theta either.

[@AryuSingh17]

how can cos30 = 3/4 😂 problem is drunk

[@Orillians]

WAS THINKING THE SAME💀

[@AryuSingh17]

@@Orillians 💀

[@motsyrhc7436]

or cos 150

[@Orillians]

​@@motsyrhc7436 Cos 150 is negative 💀

[@motsyrhc7436]

@Orillians yeah ik therefore there has to be a contradiction

[@HRRacingFan]

Guy doesn't know maths