How to solve this inverse tangent equation

Рет қаралды 4,697

Күн бұрын

Пікірлер: 23

@NamregSelaur-up4or 9 ай бұрын

You are a very good professor. You have a big an great dominium of maths. Thanks and congratulations for your teaching and sharing your knowledgement.

@PrimeNewtons 9 ай бұрын

Wow! Thank you.

@davidcroft95 9 ай бұрын

Love your excitement in explaining the solution! Wish I had a professor like you! (or all of them, school would have been funnier)

@holyshit922 9 ай бұрын

1. This notation can be confused with reciprocal 2. It is more readable to write arctan in text messages like these comments

@dituluiza1097 9 ай бұрын

Wow!Loved that.

@khairyalkhalidy1316 9 ай бұрын

Man it's amazing

@BrianLewis-r5i 9 ай бұрын

So nice 🤝

@m.h.6470 9 ай бұрын

Solution: The left term is 2tan⁻¹(x) = tan⁻¹(x) + tan⁻¹(x). Addition rules for tan⁻¹ are tan⁻¹(a) + tan⁻¹(b) = tan⁻¹((a + b)/(1 - ab)) So we end up with: tan⁻¹(2x/(1 - x²)) = tan⁻¹(1/(12x)) |tan 2x/(1 - x²) = 1/(12x) |*(1 - x²) *12x 24x² = 1 - x² |+x² 25x² = 1 |√ |5x| = 1 |:5 |x| = 1/5 case x > 0 → x = 1/5 case x < 0 → -x = 1/5 → x = -1/5 Therefore x ∈ {-1/5, 1/5}

@m.h.6470 9 ай бұрын

After the video: Basically I skipped the substitution step and went right to the last equation, by looking into my trig formula collection 😉

@amtep 9 ай бұрын

I'm not sure. tan is a periodic function, and the arctan can take values from different periods here, if x and 1/12x are in different periods. Basically, tan(arctan(x)) is only x if x is in a narrow range. There could be other solutions if you consider that. This is not one of those equations where you can just say "we only consider x in this range", because the 1/12x could turn out to be basically anything.

@TheLukeLsd 9 ай бұрын

Para a função tangente isso é correto. Mas se vc começar pela função arctangente não precisa se preocupar pq ela está definida em todos os Números Reais. E o resultado possível nos dois lados da igualdade sempre estará entre -π/2 e π/2 e quando vc fizer a tangente de algum resultado do arcotangente sempre estará nesse intervalo.

@surendrakverma555 3 ай бұрын

Thanks Sir

@Orillians 9 ай бұрын

Can you please make a video for all trignometric identities? I was able to write my solution till the tan (2 ϴ), but didnt know what to do from there, but after seeing your solution I saw that I was missing some identies. Can you pleaase cover all usefull identities? Since they help in situations like these. Thank you!

@lawrencejelsma8118 9 ай бұрын

There are scientific math tables. My sister bought awkward ones at a university bookstore but I really love the hand me down CRC tables in my bookcase! I have all geometric table identities that can be useful in solving higher problems (especially in Physics). P.S. I wouldn't really worry about this problem unless it came from a dimension at a machine shop industrial problem where real geometric problems similar to this is happening. Then you would need to be equipped with full CRC math tables books to go into getting full value of them.😊

@MrJohnBJohnson 9 ай бұрын

This Guy is the Bob Ross of math

@JSSTyger 9 ай бұрын

I get x = 0.138.

@JSSTyger 9 ай бұрын

And I'm wrong.

@JSSTyger 9 ай бұрын

error when doing the discriminant of the quadratic. It should be x² = [-2+sqrt(2304)]/1150] = 0.04 and therefore x = 0.2

@kevinmadden1645 9 ай бұрын

@@JSSTygerAlso -.2.

@GreenMeansGOF 9 ай бұрын

If you’re going to use the double angle formula, why not just use it from the beginning. Take tangent of both sides and you get the algebraic expression.