Uploaded June 2016 | Updated September 2026, 2 weeks ago
In this video we will derive the double angle identities for SIN, COS, and TAN. We will need the angle sum identities derived in the videos below:
For SIN and COS
goo.gl/Uzp7bM
For TAN
goo.gl/QRqiNf
In this video we will derive the double angle identities for SIN, COS, and TAN. We will need the angle sum identities derived in the videos below:
For SIN and COS
goo.gl/Uzp7bM
For TAN
goo.gl/QRqiNf
![Explained: Aligning Torque
Why does your steering wheel feel like it wants to straighten out when youre in a turn? In this video, Ill explain what aligning torque is, and where it comes from.
NOTES
► Im not including any mechanical trail in this description.
► The tire has no inclination angle/camber.
RELATED VIDEOS
→ Explained: Aligning Torque Simulation
https://goo.gl/NwVJjb
→ Explained: Tire Axis System
https://goo.gl/Q3w7Br
→ Explained: Tire Slip Angle
https://goo.gl/rjUcYG
THUMBNAIL IMAGE
By J.H. Sohn from Melbourne, Australia (2014 Australian F1 Grand Prix) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons Explained: Aligning Torque](https://i.ytimg.com/vi/iN9j-ff2-co/mqdefault.jpg)
![Explained: NACA 4-Digit GUI Part 1/10 [MATLAB]
This is the first video in my 10-video series on coding a program in MATLAB to compute, display, and save a NACA 4-digit airfoil. The series starts right from the beginning, and we work our way to the final code. I explain everything I do, so it should be easy to follow.
IN THIS VIDEO:
We start by opening up a new graphical user interface by typing guide in the command window, and lay out our GUI buttons, boxes, etc. After saving the GUI, we format the resulting m-file for ease of coding in the subsequent videos.
If you havent watched my other videos on the NACA 4-digit airfoil series, I would recommend doing that now.
NACA 4-Digit Airfoil Theory
http://goo.gl/IMgb1W
NACA 4-Digit MATLAB Script
http://goo.gl/t0ksgp
IN THIS SERIES:
Part 1/10 : https://goo.gl/9UBgbo
Part 2/10 : https://goo.gl/jRRcYJ
Part 3/10 : https://www.youtube.com/watch?v=SbW1NDuvdJQ
Part 4/10 : https://goo.gl/HwHB39
Part 5/10 : https://goo.gl/AlDne8
Part 6/10 : https://goo.gl/7n1QP7
Part 7/10 : https://goo.gl/nTGleR
Part 8/10 : https://goo.gl/ez247P
Part 9/10 : https://goo.gl/8mXYcc
Part 10/10: https://goo.gl/ovBlbW
For the most up-to-date GUI, download the files from my GitHub account, linked to here:
https://github.com/jte0419/NACA_4_Digit_Airfoil Explained: NACA 4-Digit GUI Part 1/10 [MATLAB]](https://i.ytimg.com/vi/iQ1-C6c3YyA/mqdefault.jpg)

![Explained: Axes GUI [MATLAB]
Axes can be used to display data on a plot, or even to display an image. This video shows how to display a plot with data in a MATLAB GUI. Explained: Axes GUI [MATLAB]](https://i.ytimg.com/vi/imyF5QjJ5c8/mqdefault.jpg)



![Explained: Sonic State (Critical, Star)
Heres the next video in our quest to understand jet engine and rocket nozzles (among other things). We will be talking about the sonic state, which is also called the critical state or the star state.
These values are useful for determining whether flow through a nozzle is choked. If the nozzle is indeed choked, then the sonic state values (P*, rho*, T*, etc.) are the actual static quantities at the throat of the nozzle.
RELEVANT VIDEOS
→ Stagnation Relations
https://goo.gl/FMFUBA
→ Area-Mach Number Relation
https://goo.gl/Hp6uGQ
REFERENCES
► Notes by Matt MacLean
► Modern Compressible Flow, Anderson
► Elements of Gasdynamics, Liepmann and Roshko
► Gas Dynamics, Zucrow and Hoffman
THUMBNAIL
By Ad Meskens (Own work) [Attribution, GFDL (http://www.gnu.org/copyleft/fdl.html) or CC BY-SA 4.0-3.0-2.5-2.0-1.0 (http://creativecommons.org/licenses/by-sa/4.0-3.0-2.5-2.0-1.0)], via Wikimedia Commons Explained: Sonic State (Critical, Star)](https://i.ytimg.com/vi/jnRudznUqDM/mqdefault.jpg)
![Explained: Waitbar [MATLAB]
A waitbar (or progress bar) allows you to visualize when a program will finish. The argument to the waitbar fills up the bar with the percentage specified. While its a fun way to see how long you have to wait until everything is done computing, it is extremely time consuming, and I would probably recommend just outputting data to the command window using fprintf. Explained: Waitbar [MATLAB]](https://i.ytimg.com/vi/k2wKPxRUPiE/mqdefault.jpg)

