Trigonometry Intro - PhysPrimer

Some basic applications of trigonometry in converting between describing a vector in terms of its magnitude and direction (hypotenuse and angle) and its x and y components (adjacent and opposite sides).
0:00 Introduction (vectors and right angle triangles)
3:01 Make sure calculator is in right mode (deg vs rad)
3:55 Pythagoras Theorem and trig function definitions
5:01 Example 1 (Hypotenuse and angle to opposite and adjacent sides)
8:45 Calculation check (which side length should be greater?)
10:00 Example 2a (Opposite and adjacent sides to hypotenuse and angle)
12:00 Calculation check (Hypotenuse should be longest side)
12:13 Example 2b (Finding the angle)
15:32 Calculation check (Is angle more or less than 45 degrees?)
17:07 Uses with other vectors
20:48 Try it yourself examples (solutions at end of description)
Opening Image Credit: NASA, ESA, CSA, STScI, Klaus Pontoppidan (STScI), Image Processing: Alyssa Pagan (STScI)
science.nasa.gov/missions/jam...
Solutions to "Try it yourself" examples (and I do recommend trying these yourself BEFORE looking at solution):
1) For 150N force:
x-component is -127.2N (negative because this vector is pointing partially to the left and the +x direction points to the right)
y-component is +79.5N (positive because this vector is pointing partially upwards and the +y direction points up)
2) For magnetic field vector:
Magnitude (hypotenuse) = 51.9uT (be careful when applying Pythagoras theorem with the negative component... when you square that negative component, the result is positive, and the hypotenuse should always be the longest side of the triangle)
Angle = 64.9 degrees below +x axis (some conventions count angles measured clockwise to be negative; I generally write the angles in this way for clarity since we might not always be measuring the angle from the +x axis as well)

[@NalitaQubit]

A genuine fan of your videos over here. Thank you for all your hard work. I grew up being told that I’m not academically smart enough which led to my disdain toward Mathematics and Physics. As a grown up, I was free from those discouraging voices, and I’m in love with Physics. Physics is my life… I love it so much.

[@PhysicistMichael]

It really frustrates me to hear stories like this (the first part, not the last part) where certain teachers' actions (intentional or not) discourage people from a STEM education because "they're not the right type of student." Learning/understanding is primarily based on how much experience you have with the topic rather than some magical inborn ability. It's why I try to encourage introduction of math and science skills at as early an age as possible, as well as better prepare teachers to effectively introduce these topics, to help give students as much of a head start as possible. But even if someone doesn't have that early experience in STEM fields, it's never too late to get started (and teachers for all age ranges should encourage this rather than writing students off).

[@Twobarpsi]

I used to get straight A's in math. Forgot it all! I even took several Calculus classes in college.

[@postiemania]

I remember this as SOHCAHTOA.

[@PhysicistMichael]

That's how I was originally taught as well. According to my students, this method is still alive and strong.