Small typo: 300 degrees=5ℿ/3

Wow, here I was spending the last hour and a half trying to memorize unit circle, not realizing whatever you Explained is the same thing the textbook was trying to explain. Thank you! It finally makes sense!

Currently, I am taking Precalculus that is crazy for 6 weeks a semester, and all I want to say that your lecture is the biggest help for me. You are the best best best teacher. Thank you, Brian

Just got into trig and everyone I know is telling me to just memorize it, and I knew there was a better way; because I've learned that in math you have to understand where the formulas and things come from or you will be lost later on. You are the only explanation I have seen ANYWHERE online that tells how to do this so I really can't thank you enough. It took me a couple of playthroughs but I know this thing completely now and can solve problems my friends have no clue how to start. Thank you, keep them comming!

Had to use my notes (completely drawn unit circle) for my whole calculus class so far, now I don't have to- this made SO much sense. I saw the patterns, this put them into a logical format, thank you!

Honestly, this whole circle thing never made any sense to me, until now. Brian so far I've used your videos to help me pass 3 separate college level math classes, BRAVO! you're a gem

I don’t get why can’t we just use a calculator. It was created to be used so let us use it. No one will ever have a job and not be allowed to use a calc. gosh.

It may also help to understand that all of the angles on the unit circle are multiples of 30° or 45°, because we use isosceles right triangle (45°,45°,90°) and the (30°,60°,90°) right triangle as a reference within the circle to derive our cos&sin values from the lengths of the triangle sides. [1, 1, 2^1/2] and [1, 3^1/2, 2] radians can seem confusing because of π . However you can use one angle to build all of the others π=180° you can look at 90° as being 1/2 of 180° therefore (1/2)π or π/2. And 45° as 1/2 of 90° and therefore (1/2)(1/2)π or (1/4)π or π/4 this works with all of the angles. 30° is (1/3) of 90° so (1/2)(1/3)π which is (1/6)π or π/6 Once you have your angles down, you can reference your two triangles and use your knowledge of the trig functions to determine your sin/cos values. However there are only 3 sets of values to remember in each quadrant, and ultimately the quadrant determines their signs. Otherwise you have the 1,0 0,1 -1,0 or 0,-1, which lie on the axises

We spent what felt like a week on the unit circle and I had no clue what to do, until you my savor taught it to me in 10 minutes the day before my exam, so thank you!

"I just don't understand, math is so hard. Can you help me with my homework?" Kid Brian: "No, Dad I have to get on the bus."

I used this method and now know how to draw the entire thing without memorization. There's a pattern that you don't even have to memorize. It's simple math. I spent less than an hour on this and can draw a full one perfectly in like 3 minutes or so. Thank you so much Mr. Logan!

Much simpler than memorizing the whole circle. However I always get a small sense of accomplishment when I complete it for tests. To each his own. Thank you for all of your amazing content, I'm getting an A in precalc because of your videos!

Going back to University in a few months and haven’t done math in 3 years so this is a great refresher. Thank you!

for negative radians you can always add 2pi, 4pi, 6pi so on to make the value positive. I think it helps

Me: Wathces the whole video Also Me: Sneaks in a post it card with the unit circle

thank you so much. it’s honestly amazing how unintuitive some companies can make trig when it’s really incredibly intuitive. Shout out to Pearson for ruining math and thank you to great teachers like this for making it crystal clear!

I was never taught the unit circle, but I did learn it this way. I completely forgot how to do it, thank you!!

Wow thank you. Would have never even thought of it that way, thank you for the awesome perspective!!

Thank you! I am studying to be a teacher of physics, yet I've had problems with memorizing the unit circle since the dawn of my trigonometry knowledge. Now I do not have to fear it anymore. Maybe I'll teach this way to my students one day :)

this helped a TINY bit, i dont know how im going to pass this year but putting those positive vibes that I will and so will everyone else here *fingers crossed manifesting*

Hello Professor McLogan! Thank you so much for this video! I now fully understand the unit circle concept after absorbing the information you have provided me with!

I've got a college trig test on Monday, No calculator, memorized unit circle. Doesn't matter if its BS.

You helped me in pre-calc algebra and still coming through for pre-calc trig. I'm so happy you exist, I'm not crying you're crying.

Thanks a lot! I found it easy to understand - you saved me from those random sin/cos/tan/etc.. questions that are gonna pop up on quizzes.

Thanks so much for this, makes a ton of sense, my teacher is MIA in my online trig class so I'm having to scour KZfaq for extra understanding 😎🤟

I cannot thank you enough for simplifying this lesson. If people only knew how much time they'd save learning this technique because it is utilised in Physics and Engineering at all levels. My own little spin on this was to cut out a circle and keep folding in half four times....then you have the exactly 16 segments.....you can fill in the whole thing based on the first quadrant...Thanks once again.

2020 and my teachers still saying I have to memorize...we need more teachers like you :)

I am currently in university. You are the man Mr. McLogan, finally found a teacher that loves their life and knows how to teach

I am in my second year of college math, and I keep coming back to your videos! Thanks for the help!

Incredibly helpful, thank you!

thank you so much! After years, I finally understand the unit circle

Your videos are always so helpful, thanks so much

You're awesome. Thanks to Organic and you, I was able to pass my PreCalc class.

Anyone here 2020? Exams coming up for me.

This was seriously helpful! Thank you so much!

Thank you so much you are definitely the best math teacher on KZfaq

Thank you, this made the unit circle much easier

mygoodness, ive spent over 4 hours (of course having breaks) trying to master this lesson with my tiny brains and now i got it ... thanks, Sir!

Absolutely awesome. Thank you for this video Mr. McLogan, learned a bunch!

5 years ago, you did a video how to memorize the unit circle. Lol. Thanks, though. I learned a lot!!

Im now in Precalc and I had alot of trouble with radians and trig and whatnot, but your video was a real help. Thank You so much for making this.

Excellent Video - great teacher, thank you!

subbed. i'm sure i'm gonna get quite familiar with your channel throughout my time in uni... keep it up man!

For the cos(-5pi/4) you can also use the property cos(-x)=cos(x) and get -sqrt(2))/2

Thank you so much.. My teacher told me to memorize the unit circle... your explanation is SOO much clearly. Cheers!

I am an Arab girl who learns mathematics from your English language channel in order to do all her exams in Arabic .. this is complicated .. but the professor’s explanation is wonderful

This is so helpful, thank you.

Very nicely done. Thank you.

THANK YOU wow that just made the Unit Circle 100 times easier to understand!!!!!!!

This really helped. I find your method of mentally visualizing the 'slices of Pi' to work well for me

What would be the angle for the measurement between 150 degrees (or 5pi/2) and 210 degrees (7pi/6)?

Omg I'm 15 and have a final exam in two days, you sir just saved my life

Thank you so much for the explanation! Although I've heard people say that you shouldn't remember the unit circle, they had never explained why.

Very helpful thanks

Thank you very much for your vid. I learned alot :D

Here you are again saving me in AP calc!

This is great. It took me 7/8th of the semester to realize that this is all on an XY coordinate system, and instead of memorizing in which quadrant sine, cosine, and tangent are positive or negative, just realize that cosine "runs along" the x-axis, and sine "runs along" the y-axis. Then sign is intuitive.

Great video, thanks for the help! Volume is pretty low, try clipping the mic higher on your collar. :)

That's really helpful, thank you!

How do you know which coordinate to use

Omg thank you for this video trigonometry is annoying when I have to learn the unit circle but this simplified it to a point where I understand it thoroughly

Sir, you are a genius!

If I pass my math 3 it’s cause of u 🥰 all credits to u !

This video is still helping people. My textbook could not relay to me in weeks what you just did in 10 minutes

thanks that was clear up to the point when you dealt with tan, found that a bit confusing....why is it adding or subtracting 2pi?

Thanks Mr. McLogan! I've been struggling to understand this concept, but now with your video I have a much better understanding! Thanks once again! Will be looking forward to watching more videos from you!

Thank you so so much for this video it was incredibly helpful for my understanding.!!!!Now i know a new handy trick :) :)

As I wait for ads to finish... PLEASE TEACH ME,THE WAYS!! Your great, thank you

I am doing my second bachelors in comp engineering at 24 i first did IT and web development and have been doing web dev informally since highschool, however i did shy away always from the math. now that i figured out i truly want to work with electronics and software i like to code but also like hardware and circuits i have to get through this math. Im currently taking precal i have a B so im only struggling a little bit out of all the online teachers or videos ive found i ve understood yours the best. so a sincere thank you sir. Do you possibly have a place where you have more dedicated videos over topics?

Respect do this man making the video while on a break

how did you get tan pie/2... 8:22 why isnt there a reference angle

This actually made Trig 10x easier for me! Thanks a bunch for this vid

What does the sin, cos and tan mean in front? Do you do these questions differently depending on the prefix?

dude ur a genius thnx really helps

My calculus teacher taught us to count to 4 from 0 (0, 1, 2, 3, 4), then square root everything (/0, /1, /2, /3, /4), then divide by 2. Start at (0, 1) and work clockwise to (1, 0) for the x value, and the opposite direction for the y value

You can also use the mnemonic ' All Silver Tea Cups' ( first quadrant : all ratios are Positive. 2nd Quadrant: Only Sin ratios are positive. Third quadrant: only tan ratios are positive and 4th Quadrant: all cosign ratios are positive.

thank you big dawg you helped

thank you sooo much!! you just saved so much of my time !!!

Thank you so much! This has really helped me

Wow, the fact that after watching this for 3 minutes and immediately being able to do any problem after forgetting everything about the unit circle from trig is amazing!

Thanks! enjoyed your insight.

I've always had the degrees and position values memorized completely. Then I just convert the degree to radian as needed. * Or realize that you can memorize the first quadrant and add pi/2 to each radian value for every 90 degrees.

Brian saving grades again.How's your little girl doing?

Do you have a video on how to remember the derivatives of trig functions because it's kinda a pain and I can't remember in a logical way like you did with the unit circle since trig is kinda weird.

good job bruh hang in there

This just saved my grade thank you !

There is no way in hell I am turning my speakers up loud enough to hear this video. I have made that mistake before and paid dearly for it. Never again.

As soon as I start leaning about the unit circle I get this in my recommended

Had trouble in precal but I got it now. However, can you go over the detail as to why? as said by others in the comment section below. Thanks

بيض الله وجهك انشهد انك الوحيد اللي يفك الزنقه

honestly, don't even memorize the first quadrant. Just envision the 30, 45, and 60 triangles in your head, specifically the length of the sides and hypotenuse, then just find the ratios between the sides of the triangle you need for your trig function. Now, the only thing you need to memorize are these 3 triangles, which is more like 2 because the 30 and 60 triangles are the same but flipped. It may be a bit more work than memorizing the first quadrant, but I find it even more logical and intuitive, which i think helps.

possible stupid question but if the rotation is more than 2pi should you always break it down by 2pi + x? In other words if it was 18pi/6, would you make it 12pi/6 + 6pi/6 and then look for pi (as the 6's cancel out)?

Brian Mclogan and The Organic Chemistry helped me to have B and A's on my exams i really hope you can help me further more in my Engineering journey ❤️❤️

Thanks for saying it I never memorizing the unit circle

really helped me get through my trig, i have ap calc as first period so i wouldve gotten whooped without this video

thank you so much u save me regularly

You're the man. Thank you very much.

Thanks for the explanation. I'll just have to memorize the first quadrant, like you said.

Thank you, so much

I hope this video comes up as a (recommended for you) to my teacher while she browsing through youtube then she'll subscribe and ring the bell and make my life great again