Why are Tangent & Secant given their names?

[SP-qoso]

I’m up at 0235 watching these videos. I’m 29, haven’t been in math classes for like 8 or 9 years, have zero use for this information, and this is still fascinating. You’re an amazing teacher.

[swag-mexico-gucci]

THE PERFECT FREEHAND CIRCLES I CAN'T

[sahibakaur]

When I watched this video, I felt that spark that I feel when I finally truly understand something without having to memorize. Thank you for allowing me to feel this through your wonderful teaching!

[tahmeedchowdhury]

Just realized this can also be used to prove the identity tan^2(x) + 1 = sec^2(x). Brilliant teacher.

[albertoolmos]

Tangent from Latin 'tangere' to touch a point, without intersecting it. Secant from Latin 'secare' to section, divide, cut something. This is why they are given their names, the rest is a mathematical convention, still sine ('sinus' = hollow) cosine (sine complement) derive from Latin too. Mathematics, as well as all sciences, are easier when you know what you are talking about.

[ermonmclovin]

Im attending engineering courses at university and ive never studied trigonometry in my entire life. Here in Italy, teachers dont care of math, they just teach greek, latin, history and humanistic stuff. Now im in a hard situation, and thanks to you im learning trigonometry not just as abstract formulas that i do not get

[rosswaring]

This guy just loves what he does. So clear and well explained with such enthusiasm. Very fortunate students to have him.

[youtert]

He's really getting off on a tangent with this history lesson.

[siddheshmadkaikar]

preparing from your videos for a competitive Engineering Exam in India, and suddenly math has become so interesting.

[HeathenGeek]

I know my way around a trig textbook, nobody ever explained tan and sec like that before.
Very, very nicely done, thank you.

[JulianAvalos]

Officially convinced some of my previous grade school teachers sucked.

[qiangqno]

wish I always have that much passion teaching every day!

[TheSidyoshi]

I am stunned, absolutely stunned. How is this possible? I have a decent grasp on abstract algebra. I was good at maths in school. I never knew where these names came from. For me tan was defined as sin(x)/cos(x) or opp/adj.

I figured it had something to do with the tangent of a circle, but wow. I'm speechless. You can reason out a lot of trig identities geometrically, just from looking for similar triangles around the unit circle!!! WOW!!!

I'm a little surprised how far in life I've come with this huge chasm in my knowledge. Now thanks to you it's been fixed up.

It's a little unnerving... what other holes are there in my knowledge?

[samuvisser]

How can this guy draw such perfect circles... It's just not fair!

[nicholasyap]

Mind offiicially blown...
How can someone be so good at explaining? Omg if he was my teacher i would have fared off so much better in math wts

[teiyaamuah]

This is one of the teachers. He makes look so easy, he is one of my best teachers. Top 5

[reintsh]

Sorry mr. Woo, you didn't explain where the names came from, so I'll do it. "Tangent" means "touching" (cf. "tangible") and "secant" means "cutting". Look at at your drawing once again and find the touching point and the cutting points. The latter are called "intersection", aren't they? Hey, SECtion, SECant?

[shubhrajit]

Thanks for your explanation! Sine has also got a similar story. My TB says "the idea of sine days back to Aryabhatta who called it jya or Ardha-jya that literally means half-chord". This is quite apparent in a unit circle.

[coldmine]

Guess what, apart from straight lines, he can make perfect circles 😂

[GigasnailGaming]

algorithm strikes again with a brilliant educator. love it. good stuff.