"Let me do another example here. Because i want to." Patrick showing everyone who's boss.

Just what I needed, thank you you're my hero now. I can't believe I pay thousands going to school and get crappy teachers who don't make sense

I've actually resorted to getting the chapter heading for my classes and then looking up your videos instead of doing their provided texts/resources. I learn faster and more completely. THANK YOU.

You just saved my life on this quiz tomorrow, you're great at explaining things clearly, especially with the abundance of examples! Thank youUuUuuUuu

I love your videos they help me so much THANK YOU!! I've been watching videos on this concept for an hour and Im just now getting it while looking at your videos. Again, THANK YOU SO MUCH!!

Focusing in on the domain subtleties is helpful. Thanks! You are making Trickynometry less tricky!

Thank you very much, nobody explains very well that numbers that don't fit the range of numbers for the cancellation formulas can still be evaluated (example C)! You explained this crystal clear!

I missed a lesson in class and was SO lost until this video! :-) Thanks for consistently great teaching!

Memorizing the unit circle is such hell.

this video helped me a lot during my junior year! our teacher teaches very well but since there are a lot of interruptions in class, its harder to understand. but when i came across your video and the previous one, i started to clearly understand and all i can say is... i'm ready for my test!

Definitely a good teacher.:)

LOVE YOU!!!!! Thank you soooooooooooooooooooooooo much!!! Seriously thought I was gonna fail Pre-Cal for this >____< You are a life saver!!!

Thanks so much for this! I have my Calculus Midterm this Friday and just needed some explaination in this. So glad you made this! Thanks again!

I've come from coming to you about simple algebra 1 things to making it here, PreCalc, with your videos. I really can't say thank you enough.

Wow, thanks for making the inverse trig function videos. My AP Calc AB teacher has assigned us to learn a several sections of Calc, one of them being Inverse trig functions. Didn't understand the book one bit, but you've created a great explanation of them.

Last minute cramming and I finally understand inverse trig! & I take my test in less than one hour! Thank you so much :)

10/10 saving my life in calculus

I go to a world-class engineering school and you are better than my professor. Thank you :)

Thank you patrickJMT YOU just helped my life so much more!!

This saved my grade! Thank you so much for making this videos.

Thank you so much for taking your time to teach us earthlings!! You even include what could be problem areas for people, meaning: "if you don't get this, then you should go back and learn it..and then it will click". Math takes time and practice, but mostly understanding through practice (trial and error). But you make it so seamless that we forget about the practice part. Just a thought for those of us who think we will remember by just doing a hard problem once. Sorry for the rant but I was inspired after this this, and again a big THANK YOU!!!!!!

8:15 it should be -pi/2 < x < pi/2 NOT the less than AND EQUAL to inequality. No worries, honest mistake. The reason is that -pi/2 and pi/2 are asymptotes so it will never equal it. :P

actually the little things that make a BIG difference in TRIG and you explained it by giving examples for the first problem when you mentioned (2.4) is undefined for sine and the 1/2 has to be between - pie/2 < ? < pie/2 .. thank you!!! for putting that in their

Great video! Really helped me out! (Also, I would suggest using a different heavier-weight marker in case you don't like those sharpie fumes)

To compute the inverse tangent of the square root of 3, I just use the 30-60-90 triangle. You just need to memorize the lengths of the legs of the triangle (sqrt 3, 1, and 2 - hypotenuse) and then to calculate tan(sqrt 3) you do opposite/adjacent of 60 degrees. Thus, the tan^-1(sqrt 3) is 60 degrees, or equivalently pi/3 radians.

thank u for the videos.u r the best teacher .u make everythng so clear and understandable.i adore u.and love u.

Thank you so much Patrick!

Yes it is very confusing to understand this right now. But the way you explained it made it so simple. Thank you :)

You're awesome!!!! I understanding so much better now. Thank! for your helped.

If it wasn't for that extra example you threw in there, I would've till been lost with Inverse of trig functions so thank you for that extra example!(:

This video just saved my life. Thank you so much!!!

Why do we use the right half of the unit circle for arcsin and arctan instead of the left half ? And why do we use the top half of the circle for arccos instead of the bottom half ?

I still don't get how for problem c you got the y variable as square root of 3 over 2??

thank you so much you really explained it well

thank you so much, i was so close to drop this class

in the min 1:40 , shouldnt that be the domain of inverse sin -1 to 1 instead of -pi/2 to pi/2 >>?? Thanks a lot

Wow these really help. Thanks man!

hello, I have a problem with evaluating something like this: arcsin(sin(sqrt(5)) Could you help with this? Thanks for million,

I thank you very Munch for explanations

Genius!!!!! thus was very helpful!! (y)

arent the domains mixed up for sin and sin^-1. im pretty sure they are the other way around

okay so arctan is kind of confusing me. why'd you include the -pi/2 and pi/2 in the domain if they are asymptotes on the graph?

At 9:39, why does pi/3 work and not 4pi/3?

hey Patrick I cant find the next video where you solve the rest of the examples? (j, k, l, m) Im trying to find out how to do the inverse trig problems with limits

"It would be easy to do (this).... But that is ABSOLUTELY NOT CORRECT" 🤣 "Lemme say it for like the...10TH TIME!" SO grateful for your clarity before my Trig Midterm man!! (😏Theys correct- youza life saver!)

Sir, can you please answer my question..... How can we understand that 2pi/3 is not coming between pi/2 & -pi/2? Please tell me. If you have any video explaining that, please send me the link. Sir, please help me. My teachers are not helping me☹️

One question, if I have a function like this, f(x,y) = (2x+3y,y) how do I find the inverse? one thing I did was switch y and z => f(y,x) = (y,x) and then I calculated them. y=y so no trouble here. x=2y+3x => x - 2y = 3x => (x-2y)/3=x so I replace and I get f(y,x) = (y,(x-2y)/3). Is this right? how can I check this ? Also ( Patrick you rock!) Thank you for all your videos!

You are the love of my mathematical life. I

Its ALWAYS the little things that nail you... Trig itself isn't bad, but there are so many little rules you have to remember.

Patrick, it's easy enough to evaluate those limits you have written (parts j,k,l,m), but how would you go about proving that those are the limits? I mean, can you show us an epsilon-delta proof?

Thnx for the videos!

is there a different way to finding ( pi/6)? instead of using the unit circle? i dont have the unit circle memorized at all...

I wish if u was my teacher , thank you all the way frome KSA❤️❤️❤️💚💚

very good teacher

thx for all the tricks...

Wait… if 2pi/3 isn't between the restrictions for arcsin(sinx), how is arcsin(sin2pi/3) not undefined? Also, I don't understand how you graphed that on the unit circle.

I don't really understand how the inverse tangent domain is -pi/2 ~ pi/2. Wouldn't that be it's range? I checked this with my calculator and doing the math out. Even other websites say that the domain of inverse tangent is -infinite ~ infinity

thank you so much for this ^^

this helps alot. thanks! :)

thanks for the video ! :)

I need the inverses of Sec, csc and cot please

I really wish you could have gone over the arccos function. I'm having so much trouble with it and there don't seem to be any explanations of how arccos(sqrt(2)/2) can even be evaluated. Since the only value with sqrt(2) in it is cos(pi/4) which equals 1/sqrt(2), not sqrt(2)/1.

I really wish that you were my teacher!): Then I would have no problems with math. You're quite awesome at teaching, by the way(:

Great video & provided a much better understanding of this topic for me! Can you clarify if the number is negative would you need to go clockwise in order to plot the solution? IE: tan -1 (-1) would the answer be -pi/4? Thanks for your help :-)

what does the Y coordinate have to do with sin? Couldn't pi/3 be juts as applicable?

i'd love to have you as my professor! Goddddd, my calc prof is so disorganized.

why we restrict the domains in inverse trigonometry

you are way better than my prof...gosh

Dear God, thank you so much for making inverse trig functions understandable!

You're amazing.

ياخ انت عجييب ايحييك ! !! that means you are awesome

I literally have no idea how I'm gonna memorize the unit circle... I've never been good at math lol. any tips?

I thought your hands are scratched (or something like that) at 9:31 . btw, thanks so much!

Ey patrick! Thank you so mucho for such helpful videosZ! I have a question, when do u know when to restrict the intervals from -pi/2 to pi/2 and 0 and PI ? when to use the correct interval? Thank you!

You are awesome omg

thank you

2.2360 is the sqrt of 5 the sin^-1 and sin cancel out welcome :)

Use special triangles it makes finding the values easier

Good for Freshmen engineering students like me bwahaha

ha, trying my best here :)

If the graph of tangent has vertical asymptotes at -pi/2 and pi/2 your restrictions on the inverse tangent CANNOT include -pi/2 and pi/2. You wrote it down as "the angle must be GREATER THAN OR EQUAL TO -pi/2 and LESS THAN OR EQUAL TO pi/2" but this is not the case.

Thanks!

Thank you

Thank you , make more sense.

definitely life saver! :D

You're usually great, Patrick, but you made that last problem waaaaaay harder than it had to be. You could have just solved for inverse of tan (sqrt 3) by using a simple 30, 60, 90 triangle with sides of 1, 2, and sqrt 3. That would have cut the explanation time in a quarter and avoided unnecessary confusion for your students.

Too much helpful video Sir but Restricted domain of arctan(x) is (-pi/2, pi/2) not [-pi/2, pi/2]

the range of arctanx is between -pi/2 and + pi/2 that is the open interval! not the closed interval you wrote

Part 5 is private :c

Thanks.. I love you..

Gracias!! :)

that is incorrect the answer is outside of the domain.. the answer here will be a complex number , also using arcsin results in an answer in radians or degrees(an angle)

Is 2.4 undefined because it passes the restrictions?

wtf... this took 10 minutes and ive pretty much learned it

perfect!

GOD HIMSELF DIRECTED ME TO THESE VIDEOS I WAS SO LOST!

I love you

No need for college. This channel's better, Haha.

👍🏻👍🏻👍🏻👍🏻

How do you get PI/6 for the angle of arcsin(1/2)? You just pop out with that answer without any explanation of how you get it. Same deal with arcsin(sqrt(3)/2), it comes out to an angle of PI/3. How? All the videos I've watched completely gloss over that, as does my textbook. Maybe I'm just retarded and not seeing something here?