Writing 30 or 60 without the degree symbol is just not right. Also, what is the range of x? If x can be any real number, the correct answer for x should be n\pi+\pi/6, n\pi+pi/3, n\pi+2\pi/3,n\pi+5\pi/6 for any integer n.

Before even looking, I smell a hidden quadratic. At least the ever-more-ubiquitous Lambert W function is nowhere to be seen! :)

@BZKnowHow

25 күн бұрын

I am glad you watched it. i can bring more Lambert W Function related problems if you are interested.

Greetings. Thanks for sharing. You made a mistake in writing down the expression. You wrote Y^2 -2Y+8Y +16 instead of Y^2-2Y-8Y+16.

@BZKnowHow

16 күн бұрын

Yes, you are right. soryy for the mistake

-2+8=10

@BZKnowHow

25 күн бұрын

thats a simple equation that you are reffering but in this perticular problem you have to incorporate sin & Cos method to solve this. Please have a look

@timpani112

24 күн бұрын

@@BZKnowHow I think the commenter is remarking on the fact that the statement is obviously wrong, and that it's something that you write in your solution. It should be -2-8=-10 at around the 3:43 timestamp, and this is indeed what you're using to find the solution to the quadratic.

sin = +- 1/2, then all the four values: 30, 150, 210 (-150) and 300 (-30) would work, not just +-30

@BZKnowHow

24 күн бұрын

nice

Overall, the solution presented gets many things right, but it contains some clear flaws that one should be aware of. If one would judge your solution on a scale from 0-10, where 10 is entirely correct and 0 is entirely wrong I reckon that your solution deserves around 3 points. Probably not below 3, maybe 4 but definitely not 5 or above. We can begin by briefly mentioning the solution to the quadratic equation established at around the 3:30 mark in the video. The solution method is completely fine, although its execution is a bit lacking here; I'm mainly talking about the error at the 3:36 mark, where you write down the erroneous statement "-2+8=10", but using some arrows. Instead of writing "-2+8" as you did, you have to write either "-2-8" or "-(2+8)", since -2+8 is equal to 6 and nothing else; I want to be very explicit on this point in particular, as I see way too many students having similar confusion when handling minus signs. This is very important: if you want to break up the term -10y into separate terms, you can't abuse notation by writing -2y+8y, as this unambiguously means something that is different from what you're trying to convey. So learn to use parentheses properly, because this kind of error is not something that any competent mathematician wouldn't notice and remark upon. Another mistake comes up at around 7:30 in the video, where roots are cancelled after which one side suddenly has a plus/minus sign before it. While all the lines that have been written down here are individually correct on their own, the kind of reasoning they make up is flawed. The square root of a number is ALWAYS the positive one (or zero if we take the root of zero) if we work on the real number line, it's never anything else. So the implicit reasoning you use in this sequence is unclear. Why not just skip the root signs altoghether? They really add nothing of value except potential confusion. If you insist on having root signs, you could write "sin x=plus/minus root of (1/4)" instead. That way, there's absolutely no confusion as to what you're actually doing to arrive at your conclusion. This kind of expositional mistake is very common among students, and all it comes down to is practicing actually conveying mathematical reasoning in text form. This is something that hurts the quality of the video in general, and a very easy fix is to actually have some text in plain English that explains what reasoning is being used between steps. Students are for some reason very reluctant to do this, but it can serve to improve the overall quality and readability of a solution many times over. At around 8:00 in the video we come to a point which I personally dislike, and that is the use of the dreadful "sin^-1" notation for the inverse sine function. Since we often write "sin^k x" to denote (sin x)^k for any number k, the notation "sin^(-1)x" becomes ambiguous, as it's not always clear whether we're referring to the actual inverse sine function, or if we're referring to the reciprocal of sin x. This is somewhat mitigated in some countries where the secant and cosecant functions are widely used to denote the reciprocals of cosine and sine, respectively, but it's far better in my opinion to just use the notation "arcsin(x)" to avoid any confusion. Besides this, the line "x=sin^(-1)(plus/minus 0.5)" is actually incorrect, and this is something that has already been pointed out before in this comment section. This is because the inverse trigonometric functions (including arcsin) are functions, meaning that they will only have one output value for every valid input value. The equation "sin x= A", on the other hand, has an infinite amount of solutions, due to periodicity (and then there's the symmetry of the unit circle to take into account). So, writing sin x=A x=arcsin(A) is just wrong no matter what A is, unless the specified range for x is a subset of the interval [-pi/2,pi/2] (or [-90 degrees, 90 degrees] if we use degrees instead of radians). So, how should you actually write these lines down to get something that is correct? The answer is actually the same as in the previous paragraph: use plain English! It doesn't have to be much, but it can make the difference between clear and completely incomprehensible: "sin x=A. Thus, due to periodicity and symmetries in the unit circle, one gets that x= arcsin A+(n*360 degrees), OR x=180 degrees - arcsin A+(n*360 degrees)." Besides the use of plain English to convey my reasoning, note in particular the fact that we get two distinct cases. You didn't include the second case, which is why you didn't find all solutions to the equation. The final error I will remark upon is the one that occurs at around 10:30. I have yet to fully understand why this one happens at all, but it's something that I've observed briefly among students that are not used to university level mathematics. You write that sin x=plus/minus 0.866. This is wrong. Plain and simple. There is no reason whatsoever to replace the root of 3 divided by 2 with a decimal approximation; it does nothing to help the solution become more transparent, it's not correct, and no mathematician would ever recommend that you do it. Yet people do this kind of thing all the time, and I really don't get it. We tend to manage to bash out this kind of thinking from our first-year students at uni pretty quickly, but I'm not sure where the general idea comes from. It really makes no sense, and if there is one thing you should just stop doing, this is it. Use exact values throughout the entire solution, and if you want to give a decimal approximation you do that at the end when all relevant calculations that need the exact values are done. You should not take this comment as a complete roast of your work - as I wrote in the beginning, your solution gets many things right, including the key ideas to solving the problem. But rather, you should take this comment as a reminder that you still have a lot of room for improvement.

@BZKnowHow

23 күн бұрын

I appreciate your passion abut learning things so deeply.

Nice! Thanks. After the discovery of x=30 (first root); I could guess the other would be 60, since by symmetry the same logic would lead to cosx=1/2 hence x could also be 60.

@BZKnowHow

24 күн бұрын

Excellent!

in squre equasina -b = x1+x2 c = x1*x2. obvious x1, x2 = 2, 8 en.wikipedia.org/wiki/Vieta%27s_formulas