@jackdunn5657
A trick we were taught in school, for secant, cosecant and cotangent, is that the 3rd letter of each represents what each one is a reciprocal of: se(c)ant = 1/cos co(s)ecant = 1/sin co(t)angent = 1/tan
@OcaRebecca
I’m a minute and a half in. You already did more to relate the unit circle to triangles than my precalculus teacher did some 25 years ago. All the unit circle was was merely a bunch of points to be memorized. Trig is a special form of hell when your teacher is constantly absent or tardy.
@Darkev77
Ooooof, I really forgot most of my HS trig stuff as I went to undergrad and grad school. I was like it’s about time I refresh my trig knowledge, and now I get Dr. Trefor’s review. Insane!
@Lhosal
I was a pure math major, didn't finish yet but I just need about 3 classes, I noticed that a lot of students in the math degrees (pure, applied, and education) struggled with a lot of fundamentals that they learned but didn't really understand in their lower education. So I didn't see students struggle with only trig, but also a lot of algebra (partial fraction decomposition, factoring, manipulating equations), exponents and logs etc. They're all essential in the most failed course during university, the class that brings it all together... calculus 2. Because it's so essential to be able to look at a cal 2 integral, and see within it, a way to manipulate it into a integrable form.
@borraginol-to-Ji
I am a Japanese college student who studied trigonometry a year ago, but I learned many more things about trigonometry today than a year ago. Thanks for this helpful video😭
@OrangeOliver-zf4sj
Thank you so much for making this video. I’m talking calc 1 next semester, but I haven’t taken precalculus/trig for about 5 years. I’ve been trying my best to review the basics and this is one of the most helpful and concise videos I’ve come across.
@SpecCtrer
This video is seriously concise, and intuitive. I feel fortunate to have started calc after it's release.
@user-ug2vw9vb2v
i'm so happy to see that this guy is finally getting the sponsorship for all the hard work he's been doing. Thank you professor!
@TommasoGianiorio
Rationalising can be useful for a fun memorization of the values for the standard angles: Root(0)/2, Root(1)/2, Root(2)/2, Root (3)/2, Root(4)/2.
@epsilia3611
6:42 One reason I found is how you have a nice pattern by doing that over the particular values : sqrt(0)/2, sqrt(1)/2, sqrt(2)/2, sqrt(3)/2 and sqrt(4)/2 are the five main values we see in high school when related to trigonometric function sin and cos, so it makes up for a very good mnemotechnical thing, so why not it's always good to take
@GregSpradlin
That unit circle diagram you showed at the beginning is the one I show my students. I call it The World's Greatest Unit Circle Diagram.
@GregThatcher
Thanks!
@johnnolen8338
The angle addition formulas are derivable almost instantly from Euler's formula: e^(iθ) = cos θ + i sin θ.
@gregwochlik9233
Nice. I high school (South Africa 1992 to 1996) I had just the few identities memorised. The rest I derived. For example, I memorised cot = cos / sin, as the two "c" went together. I remember how I "discovered" the sin(60 deg): I took my calculator in a plastic bag into the bath. I asked for sine 60 degrees, then I randomly squared the answer. I was astonished to have gotten 0.75. So, my sin(60) = sqrt(3/4).
@steve6012
if you remember Eulers and Pythagorean and that Cosine is even and Sin is odd, you can sit down with a blank piece of paper and easily (no geometry) derive angle sum, angle diff, double angle, half angle from scratch
@bigprogramming579
Oh god finally a video which explains all these topics so easily, tysm!
@cparks1000000
"Pre-calculus" needs to be abolished as a class and replaced with algebra-for-calculus and trigonometry-for-calculus, both full-semester classes. Students who are comfortable with algebra, can move directly into trigonometry. Students who are comfortable with trigonometry can just take algebra.
@DrR0BERT
Dr. Bazett, when I teach the trig of standard angles, I tell my students to rationalize their denominators for the following reasons: * It is an easy way to remember the trig of the standard angles √0/2, √1/2, √2/2, √3/2, and √4/2 for sin(0), sin(π/6), sin(π/4), sin(π/3), and sin(π/2) respectively. * When working with the radical fractions, it is easier to work GCD's when the denominator is an integer over a radical. For example, √3/2 – 1/√2 is not obvious how to combine. * When computing tangent and cotangent of the standard angles, I tell my students to ignore the 2's in the fractions. I remember when I was learning trig back in 1980, before scientific calculators found their way into our high school classrooms. Our high school math teacher had us divide 1 by 1.414... using long division. She then rationalized the denominator and showed us dividing √2 by 2 was a lot easier. Now with calculators that's no longer an issue.
@meganterry3864
This video will forever live in my saved folder. You explained it all in a way that I understand. In 20 minutes I learned more than my actual trig class. Which I had seen this video then 😄. Calculus 1 is currently ruining my life. Do you have a video like this one but for calc? I’m looking but can’t find one. My brain wants to know how everything fits together and why. What is their relationship. I’ll check out your other vids. Thank you IMMENSELY for making these.
@DrTrefor