C2 w1 derivative of trigonometric functions: phi approaches x?

in video minute 4 I dont understand why the angle phi gets equal or closer to angle x. I think that we need only show hyp h approaches delta x . Any way how is phi be equal to x?

Sorry for the delay in replying to your post.

I agree, the presentation in the video is somewhat confusing. I’ve submitted a request to make some improvements.

If you’d like to see a mathematically rigorous proof of the derivatives, please see this URL:

thanks TMosh. I searched and found method that uses limit like lim delta x->0 sin(x+deltax)- sin x/ delta x. But I wanted to understand what was in the video.

I think the video is not correct.