Thank you, I´ve never seen a demonstration like this, it's terrific.

These videos are brilliant when it comes to understanding trigonometry! You deserve way more views!

@DennisDavisEdu

Жыл бұрын

I couldn't agree more!

First time in my life (I'm 25) I have ever understood the concept of trigonometry. Not just I have learnt trigonometry, but I kinda enjoying this whole process. Every bit of new information is keeping my adrenaline moving faster, may be its because i am feeling excited to learn this new world that I was for so long absolutely ignorant of. Thank you Dennis!

@DennisDavisEdu

Ай бұрын

That's great Waqar! I'm glad to be part of your learning adventure.

Absolutely brilliant explanations. Thank you.

The visualization blew my mind. I had an "aha" moment. Thank you for this series! Really helped me in my pre-calculus course.

@DennisDavisEdu

2 жыл бұрын

That's so nice to hear, Aaron. One of the disadvantages to teaching online is that you don't get to see the "aha" moments on students' faces, so I'm glad you shared it!

Superb explanation now only I understand clearly the concept Thank you

denis you are beyond any praising word. ❤❤❤❤💯💯💯💯💯💯

There is a really general but very simple proof for all compound angle trigonometric identities for cos(a-b), cos(a+b), sin(a-b), sin(a+b), tan(a-b) and tan(a+b) with any positive or negative angles(arguments), not just positive acute angles used in most proofs. Moreover a > b or a b, and - (a - b) when a b, or -(a - b) when a

I had a series of Aha 😂😂moments.. to the point of organism. 😂😂😂thank you. So brilliant. 🙏❤🌹

Thank u sir for visualized now i understand well

Thanks very much !!!!!!

You are amazing..

🔥🔥🔥

Geometrifying Trigonometry I have made a language (parser /compiler/lexical analyser)which takes trigonometry expression as input And Converts that to euclidean geometry Then It searches hidden truths from geometry Automated theorem prover Geometrifying trigonometry Is the formal language which is cross platform communicator Platform 1 is trigonometry ecpression in latex or excel format Platform 2 is euclidean geometry My system is formalized language and framework to do this

I have a question 🙋 , why at the bottom it is adjacent multiplied by hypotenuse ? Same as for the sinus side . 😞 ( sin multiplied by hypotenuse)

@DennisDavisEdu

8 ай бұрын

Since cosine equals adjacent over hypotenuse, adjacent = cosine times hypotenuse. See TR-17.

@sheedcainiste2061

8 ай бұрын

@@DennisDavisEdu thank you 😊.

ooo im guessing this is one part that is easier to memorize than to visualize?

@Skiddla

Жыл бұрын

actually when you realize that the cos and sin of a triangle is a multiple of the hypotenuse and that the second triangles use the previous cos and sin as hypotenuses (plural?) then it becomes very clear.

@DennisDavisEdu

Жыл бұрын

It's more work, but in a pinch one could certainly re-create the construction and re-derive the identities. But yes this one might be a case where memorization is easier.

I am unable to grasp how the angle was = to alpha at 4:20

@DennisDavisEdu

Жыл бұрын

OK let's label the "bottom" angle at the point you're asking about: gamma. It doesn't have a label in the video. So there are three angles whose vertices are at the point on the right side of the rectangle. Since they sum to a straight angle, the sum of their measures must be 180°: Eq1: Right angle + gamma + the unknown angle = 180° The second triangle we slid in under the first (that includes alpha) has 3 angles. Since they are the interior angles of a triangle, the sum of their measures must be 180°: Eq2: Right angle + gamma + alpha = 180° Now from the two equations above, two expressions having the same sum (180°) must be equal. So Right angle + gamma + unknown angle = Right angle + gamma + alpha. Subtract Right angle + gamma from both sides and that leaves unknown angle = alpha

I have no idea what's going on here how is it cosa x cosb

@DennisDavisEdu

2 жыл бұрын

The length of the "bottom" side adjacent to α is cosα times the length of the hypotenuse. Since the hypotenuse's length is cosβ, this makes the length of the "bottom" side cosα times cosβ. It's the same all the way around the square in this proof: Each length is the trig function of the angle (cosine for adjacent, sine for opposite) times the hypotenuse of the triangle. And the hypotenuses are trig functions of β. So the side lengths are trig function of α times trig function of β.

Waiting half angles with animation

@DennisDavisEdu

2 жыл бұрын

That will be TR-41 but I don't know if it will be animation (geometrical) or algebraic. I haven't created the lesson yet.

@ull893

Жыл бұрын

I love geometrical. Algebraic is boring and too easy. I get aha moments in animation. Thank you.

grade a+

You are a Pitagoras reencarnation!