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Factoring confusion! Trig equation 2sin^2(x)=1, Reddit r/askmath
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- Опубликовано: 22 янв 2024
- We have to find the factoring mistake in the given steps of solving the trig equation 2sin^2(x)=1.
Original post: / uubvddjsie
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Hi!
Hi
Hi sirrr!
Hi!..... Love these videos. They give my brain more exercise than ever before.
I'm missing something here, why do we even need to factor this equation
You really don't. You just have to remember sinx will be +- sqrt (1/2) or +-sqrt(2)/2 which is all Pi/4 radians
Because it is fun.
I suppose because the original task included the erroneous factoring - you were supposed to find what was wrong with the solution. Then once you note that it's the factoring that is bad, it's helpful to demonstrate the correct way to factor, and go from there.
The correct way to factor is (sqrt(2)sinx +1) (sqrt(2)sinx -1)
ikr, thats like making it complicated for no reason-
That factoring was like "wait that doesn't work"
Inital solution has two mistakes too... It also missed the second solution for sin(x)=-1/2 (7π/6) which makes it trickier if somebody finds only second mistake but not first
-1/2 isn't even the right number. It's -1/sqrt(2) or -sqrt(2)/2 which is the pi/4's radians
@@TheChunkyCrusader yes it is not correct number what i am saying there is a sneaky second mistake after first one so you might get baited
@@TrimutiusToo yeah
if we look for 'carry over errors' and further errors
no errors were made after making the error at ii)
except for v), assuming that is the only solution.
If it was given that 2sinx + 1 = 0
then x = arcsin(-1/2) is one of the critical points then have to add integer multiples of 2pi (or subtract)
But x = pi - arcsin(-1/2) is another critical point to consider.
so step v) also has an extra mistake which carriers forward.
So there are 2 mistakes made carried over.
and i think thats what the original question was after.
Zoomed in camera? That's new, and very useful actually
He’s used it in some previous videos, maybe on his other channels. But it is a nice editing touch. I think he could just get a bigger whiteboard or clear the board along the way.🤷
I find it fun to say the answer is x = π(n-1)/4, and just define n appropriately.
1000 iq right here
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Lesson 0-4
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When factoring a² - b², do you ever need to consider if a and b are negative? I get that it doesn't matter in this example, but I'm wondering if it sometimes will add more valid solutions.
It never matters. For example you wanted to factor x^2-4.
We usually do it as x^2 - 2^2, which gives us (x-2)(x+2)
Suppose you write x^2 - (-2)^2. You get [x-(-2)][x+(-2)] = (x+2)(x-2)
Suppose you write (-x)^2 - 2^2. You get
(-x-2)(-x+2)
= [(-1)*(x+2)] [(-1)*(x-2)]
= (-1)(-1)(x+2)(x-2)
= (x+2)(x-2)
If you used both -x and -2, you still get the same factoring.
Can someone explain that when the answer is 3pi/4 why it should not be pi as ther is 135 + 45 = 180 = pi and in 7pi/4 not 2pi as 315 + 45 = 360 = 2pi
beautifully done.
I might have asked this in a previous video, but what is the square root of 2? What do you times by itself to get 2?
Since 1*1 = 1 and 2*2 = 4, the square root of 2 must be somewhere between 1 and 2. In fact, sqrt(2) is approximately 1.41421…
@@dethmaiden1991 That's crazy that a decimal like that would ever be needed in any calculations.... And it's also crazy that a decimal just shy of 1.5 timed itself would equal 2.
@@dethmaiden1991 But this is what they call an "unclean number." Or something like that.
@@JubeiKibagamiFez it’s famously an irrational number, which means it can’t be written as a fraction using two whole numbers. This also means that the decimal never ends and never repeats.
@@dethmaiden1991 Wow.
I'm only in 10th and managed to find the mistake and get the correct answer. 🔥
Me too. Where are you from?
Recognizing double angle formula for cosine would be correct way to solve it
While you are correct, depending on the grade level of the questioner, this may be beyond their experience. Schools in Ontario, Canada don't teach double angle formulas until well after introducing quadratic trig equations. The latter is done in Grade 11, and the former in Grade 12.
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@@Fynedge Well, I think the correct one is just rearranging to sin^2(x) = 1/2 => sin(x) =+/- 1/sqrt(2) Don't know why anything more complex is needed
@@silver6054 You're right, nothing else is needed. But it is an opportunity to show the hows and whys of the +/- thing. Plus, this approach can help in other types of questions. I'm blanking on an example, off the top of my head, but they do exist.
The mistake is the no. 2 step.
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Alternate solution:
2 sin²x-1=0
(Add +1 on both sides)
2 sin²x=1
(Divide by 2 on both sides)
sin²x=1/2
(Finally square root on both sides)
sin x=√1/√2
sin x=1/√2...........ANSWER!!!
Some of the ANSWER!!! You forgot the negative possibility and have to do the inverse sine to get the actual answer