Love all you teachers who take the time to do this stuff. Seeing from multiple demonstrations makes it almost impossible to not ace these classes. Thank you
As I'm preparing for my college placement tests, I came across my college's review guide. The guide gave a helpful tip to remember what stays positive in what quadrant. All Students Take Calculus, which translates into... All trig functions are positive in quadrant I, sine is positive in quadrant II, tangent is positive in quadrant III, and cosine is positive in quadrant IV. This video helped me out so much! Thanks :)
Very clear explanation! I'm taking an online Pre-Calculus class and was getting confused as to when you would subtract the reference angle from pi or 2pi. Your video helped illuminate this concept for me, thank you very much!!
You are an amazing teacher! You made understanding math so much easier for me in the matter of minutes. Please continue what you do because you are great at it. I am really thankful!
You have to memorize the exact values for sine, cosine, and tangent of 30, 45, and 60 degrees. That way you know that cosine, 30 degrees, and sq rt 3/2 all go together.
You may also think of it in these terms: sin means y on the coordinate plane. The angles are measure from the horizontal x-axis, and 60 deg is greater than 30 deg, therefore root 3/2 is greater than 1/2. cos means x. Also remember that sin starts at zero at 0 deg and goes to 1 at 90 deg and thus the numbers for it in Quadrant I must increase as you go up. cos goes from 1 to 0 in Quadrant I and therefore gets smaller as you go. tan goes from 0 to undefined so it goes 0, rt 3,1,rt3/3, undefined.
An easier way to memorize the unit cicle: In the first quadrant its all positive. So if you get a positive answer like sinx=1/2 then one of the answers are 30 degrees or pi/6. The second quadrant is 180-x so to find the second solution its 180-30=150. In the third quadrant its 180+X and in the fourth 360-X. If the equation is on cosx then the answer will be on the first and fourth quadrant. If uts negative it will be on second and third.
Thanks again, Love your stuff and show bits of these to my precalc class. This reinforces their learning and exposes them to alternate explanations... jc
trig is a cancer lol it wasn't fun at all lol its just like that annoying person that comments on a comment from 8months ago!!!! lol hahhaha 😂😂😂😂😂😂😂😂😂 well good luck this semester Nicole 😉😉😉😉
fun fact: part 1 of this series (this very video) was uploaded in November 2007, part 2 was uploaded in March 2012 and part 3 was uploaded in January 2013. I guess the 2 latter parts were possibly removed and re-uploaded.
Isn't sine positive in quadrants one and two? You said quadrant three, but you wrote it in quadrant two, so probably just a slip of the tongue. (I'm referring to the second example you did around 4:43)
I'm 11 years old and I know Integrals ,derivates, limits, Trig equations , quadratic equations,linear equations, unit circle, Trigonometry on right triangle, Logarithmic equation , cubic equations , absolute value equations, area and perimeter , definide integral, polynomials , dividie polynomials ,(multiply)(sum of polynomials, diferenc) , Differencial of function , double derivate , triples derivates ...
here is a simple way to remember all the reference angles of all the theta just remember the sin theta 0 degree - o 30 degree - 1/2 45 degree - 1/root of 2 60 degree - root of 3/2 90 degree - 1 The cos of theta will be the opposite of sin theta i.e 0 degree - 1, 30 = root of 3/2, 45 =1/root of 2 ,60 = 1/2 ,90 - 0 now divide sin theta by cos theta and you will get tan theta i.e= 0/1=0 , 1/2 / root 3 / 2 = 1/root 3, 1/ root 2/ 1/root 2=1, root 3 /2/ 1/2=root3, 1/0=not defined
k is just a variable like in regular y=ax equations, in which x (or in this sense k) represents a number that changes. As the person above me said, the changing number of revolutions is what k would be. So if you want to know the radians or degrees to travel if you're going 5 revolutions instead of 1, then we would plug 5 in for the equation, so T=330+360x5 and T=30+360x5!
It's wrong to write your reference angle as theta, because then you are technically saying that theta is equal to your reference angle. This is only true for quadrant 1, as for other possibilities of theta, it would only be equal to however many degrees minus your reference angle.
anyone wanna help me....5cos^2 (theta) - 2.5 = 0 then i got to cos theta = square root of one half..which is 45 degrees using the inverse function. so i now have my reference angle...the range is 0
I know this is besides the point (thanks for this video :D) but man, you should be Santa Claus for christmas~ I can imagine your voice going "ho ho ho" and being all jolly :)
THESE ARE THE TEACHERS WE NEED IN AMERICA!!!!!!! FIRE ALL THE CRAP ONES WHO WANT YOU TO FAIL. THIS GUY ACTUALLY WANTS TO HELP YOU UNDERSTAND MATH
Love all you teachers who take the time to do this stuff. Seeing from multiple demonstrations makes it almost impossible to not ace these classes. Thank you
As I'm preparing for my college placement tests, I came across my college's review guide. The guide gave a helpful tip to remember what stays positive in what quadrant. All Students Take Calculus, which translates into... All trig functions are positive in quadrant I, sine is positive in quadrant II, tangent is positive in quadrant III, and cosine is positive in quadrant IV. This video helped me out so much! Thanks :)
You sir, are a life saver.
My trig teacher hardly speaks english, where has this been all year!!
I DID NOT UNDERSTAND THIS UNTIL I WATCHED THIS VIDEO. I cannot thank you enough.
Very clear explanation! I'm taking an online Pre-Calculus class and was getting confused as to when you would subtract the reference angle from pi or 2pi. Your video helped illuminate this concept for me, thank you very much!!
like if you have a test tomorrow, thats why youre watching this.
its a life saver
Missed school today, have it tomorrow .-.
Skyline Busta quiz actually
homework.--. LOL
yup
You are an amazing teacher! You made understanding math so much easier for me in the matter of minutes. Please continue what you do because you are great at it. I am really thankful!
that's what i usually tell my students.....
You get wisdom from older peeps!!!
u rock sir!!!
keep on posting helpful vids
awesome teacher. dont know him in person, but i've been using him for 2 years on youtube when i need a refresher. thanks for the help stranger! =)
i've seen many of your videos and every time i watch them, i understand it. you are probably the coolest math teacher THANKS!
Just amazing. If I had had him teaching me from the beginning I would not have failed my maths exam.
I actually watched this for fun, more as an old review and I now understand better then ever! Thank you (:
You have to memorize the exact values for sine, cosine, and tangent of 30, 45, and 60 degrees. That way you know that cosine, 30 degrees, and sq rt 3/2 all go together.
OMG I LOVE this bloke. 4 hours of lecture couldn't do what he did in 7 minutes.
You may also think of it in these terms:
sin means y on the coordinate plane.
The angles are measure from the horizontal x-axis, and 60 deg is greater than 30 deg, therefore root 3/2 is greater than 1/2.
cos means x.
Also remember that sin starts at zero at 0 deg and goes to 1 at 90 deg and thus the numbers for it in Quadrant I must increase as you go up.
cos goes from 1 to 0 in Quadrant I and therefore gets smaller as you go.
tan goes from 0 to undefined so it goes 0, rt 3,1,rt3/3, undefined.
Youre one of them... Those teachers who love covering the board
Thank You I have Problems In My trig class And we are currently using your Textbook This is really helpful THANKS. +K
now, i need a physics version of this channel.
brilliant! concise, direct, no bullshit attitude. Great teacher
sec, cot and csc are simply reciprocals of sine, cos and tan. sec=1/cos, cot=1/tan, and csc=1/sin.
Hope this helps you.
Thank You so much, you teach really well, and it really helps. A really big help!!! Thank you! All the Best
this is a wonderful video lesson..
the lesson motivated me to emulate this mode of teaching, kudos...
An easier way to memorize the unit cicle:
In the first quadrant its all positive. So if you get a positive answer like sinx=1/2 then one of the answers are 30 degrees or pi/6. The second quadrant is 180-x so to find the second solution its 180-30=150. In the third quadrant its 180+X and in the fourth 360-X. If the equation is on cosx then the answer will be on the first and fourth quadrant. If uts negative it will be on second and third.
Thanks again,
Love your stuff and show bits of these to my precalc class. This reinforces their learning and exposes them to alternate explanations...
jc
Great Video. You do a great job explaining
His smile is calming
4:36 you want the reference angle in quadrant TWO not quadrant three. Sine is positive in quadrants 1 & 2.
your lessons are highly appreciated
It would probably depend on what your instructor prefers. In my trig class, we exclusively use radians.
You're right. And so the quadrant that he ended up placing the reference angle in. I think it was merely a mind slip :)
If you find an answer to that you tell me where people are really going to need this in the real world
I want you as my teacher. Why aren't my profs like you?
Thank you x 1 000
Lots of help, saved my grade!!!
@super1range He had root three over two, that's a 30, 60, 90 degree triangle. Since the opposite side is 1, you know that the interior angle is 30.
thank you! this is so helpful because i have a test on this tommorow!
it was so difficult to understand before.but at last i anderstood!!thank you sir
excellent explanation...thank you for the videos..
That means your calc is in the wrong mode. Press mode and go down to radians, then press enter. Currently, your calc is in degree mode.
hey! thanks this really helpful its help me a lot
i'm terrible in math speacial graph
Thank you. you are an awesome teacher!!!
Great video, I needed the clarification.
This will help me a lot. Thank you.
Nice presentation. The part that I keep on getting lost is when you draw these lines graphs.
dude within the first 2 minutes you made me understand so much more. I have decided to make you my god. Thank you savior of m math average.
+Nicole Nicoleo Nicole has a crush lol jk!!! but im pretty sure everyone likes him
trig is a cancer lol it wasn't fun at all lol its just like that annoying person that comments on a comment from 8months ago!!!! lol hahhaha 😂😂😂😂😂😂😂😂😂 well good luck this semester Nicole 😉😉😉😉
Crizzly 16 you too! remember that grades don't define your intelligence!!!
for sure😉😉😉 that is why im quitting school an start my own company lol!!! well have and awesome night 👌👌👌
how has it been going?
fun fact: part 1 of this series (this very video) was uploaded in November 2007, part 2 was uploaded in March 2012 and part 3 was uploaded in January 2013. I guess the 2 latter parts were possibly removed and re-uploaded.
Just in time for my math test. Thanks!
Very good explanation!
this teacher reminds me of my maths teacher, mr waters
Isn't sine positive in quadrants one and two? You said quadrant three, but you wrote it in quadrant two, so probably just a slip of the tongue. (I'm referring to the second example you did around 4:43)
Quick question all: Could you also use -30 degrees instead of +330 degrees? Thanks!
+ib3scope yes sir
I'm 11 years old and I know
Integrals ,derivates, limits, Trig equations , quadratic equations,linear equations, unit circle, Trigonometry on right triangle, Logarithmic equation , cubic equations , absolute value equations, area and perimeter , definide integral, polynomials , dividie polynomials ,(multiply)(sum of polynomials, diferenc) , Differencial of function , double derivate , triples derivates ...
so you will always get 2 answers between 0 and 360 degress and add 360k to each of them to get the infinite solutions, right?
Thank u ! My teacher didn't explained that part. :D
here is a simple way to remember all the reference angles of all the theta
just remember the sin theta
0 degree - o
30 degree - 1/2
45 degree - 1/root of 2
60 degree - root of 3/2
90 degree - 1
The cos of theta will be the opposite of sin theta i.e 0 degree - 1, 30 = root of 3/2, 45 =1/root of 2 ,60 = 1/2 ,90 - 0
now divide sin theta by cos theta and you will get tan theta
i.e= 0/1=0 , 1/2 / root 3 / 2 = 1/root 3, 1/ root 2/ 1/root 2=1, root 3 /2/ 1/2=root3, 1/0=not defined
explained this better than my teacher
yes! thank you I was completely stymied on the cosx=-3 part
his voice is so calming
this makes so much sence thankyou!
In your graphs, how are you calling 2x = 2pi/2 = to PI?, in other words how are you calling 2X=2PI over 2 = PI
so for the problem 2 cos theta-1=0 would the answer be 60 and 300 (degrees?)
@083Abhi i think u need to multiply them the simplify it u will be able to prove it
@JuTimberlake that does not work... it just says error:domain when i press enter
I still don't get the k at the end
The k is just how many revolutions you go. So sin(30°)= sin(30°+360°).
k is just a variable like in regular y=ax equations, in which x (or in this sense k) represents a number that changes. As the person above me said, the changing number of revolutions is what k would be. So if you want to know the radians or degrees to travel if you're going 5 revolutions instead of 1, then we would plug 5 in for the equation, so T=330+360x5 and T=30+360x5!
this really helped...thanks brother
can u prove
sec A (1-sin A) (sec A+ tan A)= 1
by solving right hand side
Thumbs up to this guy!
Thank you. This helped me a lot.
You sir, are a good man
Very helpful! Thank you very much!
It's wrong to write your reference angle as theta, because then you are technically saying that theta is equal to your reference angle. This is only true for quadrant 1, as for other possibilities of theta, it would only be equal to however many degrees minus your reference angle.
you make math easy on my brain
anyone wanna help me....5cos^2 (theta) - 2.5 = 0
then i got to cos theta = square root of one half..which is 45 degrees using the inverse function. so i now have my reference angle...the range is 0
thank you for saving my grades :-)
@baderocks2 my god.. we should be given so much more credit for even being able to fathom some of this stuff!
My teacher wants everything in radians, not degrees. Its remembering the radians on the unit circle that always confuses me
Sin is positive in quadrants 1 and 2
I know this is besides the point (thanks for this video :D) but man, you should be Santa Claus for christmas~ I can imagine your voice going "ho ho ho" and being all jolly :)
Heartiest Greetings!
@S2DAHZ1 in the calculator, press cos^-1 and then the value, here it's square root of 3 over 2, and then enter (=), and it'll give u the ref angel
thanks alot, your explained that very well!!
its kinda confusing when he said that the big angle in the beginning is 330 when
360-(30+30)=300
You have filled in the missing links for me thanks!
you are so very helpful, ty
so is*
he said sine is positive in quadrants 1 and 3 instead of 1 and 2 around 4:40
didnt exactly help me directly but now i know what the hell my textbook is trying to tell me
How did u derive your reference angle?
Nvm its inverse cos
which number do you sub into K?
same. This guy is great!
not a big deal, but he keeps saying Quadrant III in the second problem, when he is using Quadrant II (4:40)
I think the answer to the last equation was -1. ; -5+2=3cos theta
damn tomorrow is my exam day and im learning this now ...
beautiful!
if its cos^2 (2x) is being underroot.. does it become cos 2x or the 2 from the 2x is also rooted?.__. #RIP language
thanks alot this helped me alot
can u get anymore original?
You didn't explain where you got 30 degrees.
Why is it 30 degrees?
because cos underroot 3 over 2 is equal cos 30 degree
thank you ver much :) it hleped me understand it moree...