Why is sin²x + cos²x = 1 ?

Explanation on why sin²x + cos²x = 1 using a right triangle.

[thomasnartey]

Thank you. For about 20 years now I finally understood this

[mr.m]

This is how I admired one of my proffesor in College . He is very good showing how equations and formulas were derived. Sir you are so amazing. More video of this kind please.

[hertselcorech]

Beautiful, thank you Mr. H, it's always a pleasure to watch your lectures.

[dragoscalin]

Da, în liceu, învățam asta mecanic, pur și simplu nu înțelegeam de ce este așa, însă dacă stau bine și mă gândesc, nici nu mă întrebam de ce este așa. Acum, când au trecut anii și nivelul de înțelegere este altul, iar pasiunea pentru matematică nu a încetat, ba din contră, s-a accentuat, a sosit și plăcerea de a înțelege cum stau lucrurile. Vă urmăresc continuu D-le profesor pe D-tră și pe alți pasionați ai matematicii, recapitulând cât mai mult posibil și învățând multe alte lucruri de la D-tră. Vă doresc sănătate și succes în continuare.

[LogicApparatus]

He does a good job of explaining the subject to us pupils, let us respect our master :)

[SenthilKumar-znmu]

I am 53 yrs with medical profession
Loves a lot ur video and impressed!

[paulfrank]

I used to derive this from the unit circle. But, I like this proof better. My way only proves the equation when the hypotenuse is 1. But your proof proves it for all right triangles.

[wlbwjln]

Thank you Mr H for your time and effort in making these videos. Please continue to do so as they are both informative as well as educational.

[HA-sxtr]

Brilliant man .
His way of teaching is marvellous.

[CR_thegoat]

Although I knew that already but I still wanted to watch your proof of equating. Thank you Mr.H

[MeMadeIt]

Thx MrH!
Just accepted it as true and never considered "why" is was. 🤔

[ladyM]

Your lessons are so good and clearly explained. Love it. ❤

[bryanalexander]

(sin(x))ⁿ=sinⁿ(x) and (cos(x))ⁿ=cosⁿ(x) for n≠-1.

Personally, I use arcsin and arccos, because I do not want to get them confused with csc and sec.

Of course, it is probably the exponent that is out of the norm though, since (f(x))ⁿ is not written as fⁿ(x), rather that indicates the nth derivative, so I am quite comfortable with f-¹(x) being the inverse of f(x).

[BOT_Gamez]

That screen board is very different. Amazing technology!, projector projects words written by pen on just simple board. Quite asthetic.

[mohindersinghchahal]

Thanks Brother. I am proud of your teaching. Your teaching is very interesting and well defined to the Subject.

[davidshechtman]

Basic Pythagorean theorem but what has never been explained throughout the ages is why does the Pythagorean theorem hold? What is it about a right triangle that ensures that the squares of the legs always add up to the square of the hypotenuse?

[vernonthiede]

Got to Love Mr. H for making things so simple!!! I believe I can remember this one for life now.

[KingAeetes]

Excellent explanation. Very clearly communicated. Many thanks!

[Ghøßt]

Can you also do the other identities or is it the same... like, do we just have to separate a^2 and b^2 as you did for c^2 and divide and further?

[venturabushcraft]

Can you do a series of videos on Dirac notation sir. Bra ket notation is used for quantum computers. Vectors and matrices operators in Hilbert space. Thank you for your lessons. 👍