We just started doing trig equations in school and I realised how fun it is to play around with trig identities. Really glad I found this video, it was really fun and I became more familiar with with other trig functions than sin, cos, and tan, which are the ones we've manly had thus far.
Finished the video now, took some breaks in between. Was able to get most questions on my own but it was really fun to see how our ways of solving them differed. Especially on questions 16 and 17 I overcomplicated it a lot but I did end up at the right answer. Tank you so much!
42:40 I am with you brother. I am doing my best on the problems and you're filling in the gaps as I work on this over the course of a few days. Your videos have been valuable to my efforts to strengthen my math skills. Thank you very very very much BpRp!
Thank you so much for explaining well, I was assigned this today and was so confused and SCARED haha. Watched over 2 of your problems and I'm starting to understand!
I ran into an interesting trig problem on my no calculator pre-calc/alg 2 test and was wondering how to do it since I only had solutions and all my teachers said there had to be a trick they didn’t know. The problem was If sin(x)+cos(x)=1/3, what does ((sin(x))^5)+((cos(x))^5)=
@@adamhurt6140 I figured it out. The answer was 344, but thats cause they asked for the answer in fractional form (k/w), and then the answer is k+w. thats obviously not a critical step, so I didnt include it. If you want to know, u take pascals triangle and expand it out with sin(x) and cos(x), isolate sin^5(x) +cos^5(x), then factor and break down the rest of it using trig identities and the given. Also have to realize that since sin(x)+cos(x)=1/3, cos(x)*sin(x)=-4/9. thats also key
Q17: [tan(x)+tan(y)]/[1-tan(x)tan(y)]=tan(x+y). So, tan(x)+tan(y)=tan(x+y)[1-tan(x)tan(y)] Is it necessary to reduce to sines and cosines? {sin(x+y)[1-(sinx/cosy)*(siny/cosy)]}/cos(x+y)=sin(x+y)[cos(x)cos(y)-sin(x)sin(y)]/[cos(x+y)cos(x)cos(y)]=sin(x+y)cos(x+y)/[cos(x+y)cos(x)cos(y)]=sin(x+y)/cos(x)cos(y)
26:20 It is unbelievable that even the GOAT of Mathematics, who alone is strong enough to beat Lord Wolfram|Alpha, is lagging!!!!!!!!!!! THIS IS ALARMING FOR THE DIMENSION OF MATHEMATICS!!!!!!!!!!!!
Just for geeks like me watching this video... Here's a stupid math idea I created to calculate solutions for cos(x) returning bigger numbers than 1 just calculating them in your head: There's multiple solutions that can be calculated in your head, but this is a puzzle for you guys... (I'm an a*hole ;P) Lets take 17... its odd number. divide by 2 and round it down&up to get 8&9 => a=17; b=8; c=9: cos(17)=cos(ln(17+12sqrt(2))i) a: 17 b: factors made by 2*2*2 so we can get 2 out of sqrt leaving just 2 inside c: factors made by 3*3 so we can get 3 out of sqrt leving just 1 insede d: left out of sqrt multiplied 2*3=6 e: left inside sqrt multiplied 1*2=2 cos(a)=cos(ln(a+2d*sqrt(e))i) Lets take 100... its even number. add and subtract 1 to get 99&101 => a=100 b=99 c=101 cos(100)=cos(ln(100+3sqrt(1111))i) a: 100 b: factors made by 3*3*11 so we can get 3 out of sqrt leaving just 3 inside c: factors 101 e: left out of sqrt mutiplied 3 d: left inside sqrt multiplied 11*101=1111 cos(a)=cos(ln(a+b*sqrt(d))i)
Could someone please help me do the time stamps because it will really help all the viewers to navigate the video? I will also credit your name in the description. Thank you.
@@blackpenredpenHey I am taking AP precalculus, we are over hallways through unit 2 and it doesn't seem too bad. any suggestions on how to master my algebra (especially algebra 2) skills that are lacking from having those classes over zoom. Thank you 🙏
Hi backpenredpen!!! You always keep me motivated to record math videos!!! Sometimes I ask myself why should I continue making math videos on youtube, but then I watch one of your videos and they inspire myself to do it!!!🤗🤗🤗
Love you sir....❤️❤️❤️ From india We aren't studying Trigonometry.. But i understood all you taught.... On the 14th question i think we can simplify it to Cos(x)Cos(2x)=2Cos³(x)-Cos(x) Its heartbreaking to see the expression being not factorised... 🤣🤣 Any way.. Big fan sir You are wonderful...🔥🔥❤️❤️ (And Happy teacher's day also❤️)
24 Trig Problems done in *one* take, that's gotta be BPRP, aka 'The Beast'. Identity mathematics presented the way we spoilt brats have grown used to. Don't take this man for granted, though!
for q6 an alternative solution would be to take the -1 as being equal to -sin^2(x)-cos^2(x) (multiplying original identity by -1) and substituting, then simplifying the equation down to sin^2(x) really helpful video, i love all your tutorials
Happy Teacher's day Sir. Today 5th September every year in India we celebrate Teacher's Day to so our love toward the teachers. Your lecture are just brilliant i following your channel since 2020.thak you sir for everything.
I would love it if you’d do some extra identities for the parabolic version of trig fies. So cosp and sinp identities! Why? Cause they behave somewhat different than the normal sin/cos and hyperbolic sinh/cosh versions!
I don't understand why he puts cos3x = (cosx)(cos2x)..This seems wrong, because for example, cos 60 = o.5, but cos 20 is .9397 and cos 40 is .766, and multiplying these these gives an answer of of .7198. which is nowhere near .5 ! Can someone please explain? I Thanks
Further to mt previous reply, can you please tell me if there is any way available to derive the formula cos (A + B) = cos A.cos B - sin A.sin B ?@@AttyPatty3
My Lord!!! Thank you very much!!! You had simplified my life!! I’m back in school after many years, and I was struggling into I found your video!!! Where did you got the T-shirt and the table you have on the wall??? I appreciate your time, dedication and advice!!!
I'm taking AP Precalculus this year and so far its not bad. So far its just been obtaining a deeper understanding of functions and what values can be obtained from the equation of a function.
Timestamps below 😊😊
1) 0:32
2) 4:42
3) 7:15
4) 9:04
5) 10:47
6) 13:01
7) 15:36
8) 19:10
9) 24:12
10) 29:33
11) 32:40
12) 36:55
13) 42:46
14) 45:41
15) 49:41
16) 57:25
17) 1:02:07
18 ) 1:04:49
19) 1:07:29
20) 1:12:09
21) 1:16:11
22) 1:14:50
23) 1:20:21
24) 1:23:58
100 differential equations please❤❤
Thank you!!!!!!
@@blackpenredpen please make a video about
Digamma (x)=1
We just started doing trig equations in school and I realised how fun it is to play around with trig identities. Really glad I found this video, it was really fun and I became more familiar with with other trig functions than sin, cos, and tan, which are the ones we've manly had thus far.
do 200 trig equations/inequalities in one take as fast as you can 😂😂
Jesus loves you ❤️ please turn to him and repent before it's too late. The end times described in the Bible are already happening in the world.
make it logarithmic equations/inequalities LOLL@@L17_8
I wish he doooesss I'm currently self studying trigonometry and this would be so helpful
Listen to the very last line of "Alphabet Aerobics" by Blackalicious and you'll know why I think you should.
@@L17_8if Jesus was a carpenter then he used trigonometry. Why didn't they write that trig down in the Bible? I'm just asking questions.
Finished the video now, took some breaks in between. Was able to get most questions on my own but it was really fun to see how our ways of solving them differed. Especially on questions 16 and 17 I overcomplicated it a lot but I did end up at the right answer. Tank you so much!
Glad to hear. Thank you, too!
42:40 I am with you brother. I am doing my best on the problems and you're filling in the gaps as I work on this over the course of a few days. Your videos have been valuable to my efforts to strengthen my math skills. Thank you very very very much BpRp!
Glad to hear!! Keep up your good work and best wishes to you!
Thank you so much for explaining well, I was assigned this today and was so confused and SCARED haha. Watched over 2 of your problems and I'm starting to understand!
Thanks professor ! Please also make video on analytical geometry
Many THANKS for all the time you put into your videos. I find you inspirational 😁
I definitely loved your math questions ❤😮
i am a 12th grade student in Turkey and these questions are way easy than I expected.
49:24 "If I did my math right" - If this man makes mistakes in addition, I am allergic to numbers
at 14:37 sir you can also write 2sin^2(x) as sin^2(x) + sin^2(x) + cos^2(x) - 1=sin^2(x)
I ran into an interesting trig problem on my no calculator pre-calc/alg 2 test and was wondering how to do it since I only had solutions and all my teachers said there had to be a trick they didn’t know. The problem was
If sin(x)+cos(x)=1/3, what does ((sin(x))^5)+((cos(x))^5)=
what was the answer they gave you?
@@adamhurt6140 I figured it out. The answer was 344, but thats cause they asked for the answer in fractional form (k/w), and then the answer is k+w. thats obviously not a critical step, so I didnt include it. If you want to know, u take pascals triangle and expand it out with sin(x) and cos(x), isolate sin^5(x) +cos^5(x), then factor and break down the rest of it using trig identities and the given. Also have to realize that since sin(x)+cos(x)=1/3, cos(x)*sin(x)=-4/9. thats also key
I am doing to do your test to repeat for my school test... i will tell you how it will go
1:06
if u look at the captions..
cosx over se-
Hai sir can you discuss telescopic sums with alternating positive negative sums
Bro you are awesome I love you ❤❤ I am from india and I am like maths
Thank you!
Bro can help me a little bit
You deserve more views man.
26:34 Bro acts like he just made the height of 2 tall buildings approach 0m in 2001
I like this a lot. Thank you my friend.
Q17: [tan(x)+tan(y)]/[1-tan(x)tan(y)]=tan(x+y). So, tan(x)+tan(y)=tan(x+y)[1-tan(x)tan(y)] Is it necessary to reduce to sines and cosines?
{sin(x+y)[1-(sinx/cosy)*(siny/cosy)]}/cos(x+y)=sin(x+y)[cos(x)cos(y)-sin(x)sin(y)]/[cos(x+y)cos(x)cos(y)]=sin(x+y)cos(x+y)/[cos(x+y)cos(x)cos(y)]=sin(x+y)/cos(x)cos(y)
My take:
1. sinx +cotxcosx = sinx +(cos^2x/sinx) = (sin^2x + cos^2x/sinx) = 1/sinx = cscx
2. (1-cos^2x)/sinxcosx = tanx
3.cosx/sinx(1/sinx - sinx) = cosx/1-sin^2x = secx
4:1+2cosx/2+secx = 1+2cosx/2+1/cosx = cosx+2cos^2x/2cosx+1 =cosx(2cosx+1)/2cosx+1 = cosx
5:1+sinx/(1-sinx)(1+sinx) + 1-sinx/(1-sinx)(1+sinx) = 2/cos^2x = 2sec^2x
plz teach mathematicalinduction
Good teacher watching from india guys reply where are you watching from?
I like your Nepal flag.
you're amazing thanks
Ok time to do some maths
26:20 It is unbelievable that even the GOAT of Mathematics, who alone is strong enough to beat Lord Wolfram|Alpha, is lagging!!!!!!!!!!! THIS IS ALARMING FOR THE DIMENSION OF MATHEMATICS!!!!!!!!!!!!
Just for geeks like me watching this video... Here's a stupid math idea I created to calculate solutions for cos(x) returning bigger numbers than 1 just calculating them in your head:
There's multiple solutions that can be calculated in your head, but this is a puzzle for you guys... (I'm an a*hole ;P)
Lets take 17... its odd number. divide by 2 and round it down&up to get 8&9 => a=17; b=8; c=9:
cos(17)=cos(ln(17+12sqrt(2))i)
a: 17
b: factors made by 2*2*2 so we can get 2 out of sqrt leaving just 2 inside
c: factors made by 3*3 so we can get 3 out of sqrt leving just 1 insede
d: left out of sqrt multiplied 2*3=6
e: left inside sqrt multiplied 1*2=2
cos(a)=cos(ln(a+2d*sqrt(e))i)
Lets take 100... its even number. add and subtract 1 to get 99&101 => a=100 b=99 c=101
cos(100)=cos(ln(100+3sqrt(1111))i)
a: 100
b: factors made by 3*3*11 so we can get 3 out of sqrt leaving just 3 inside
c: factors 101
e: left out of sqrt mutiplied 3
d: left inside sqrt multiplied 11*101=1111
cos(a)=cos(ln(a+b*sqrt(d))i)
Could someone please help me do the time stamps because it will really help all the viewers to navigate the video? I will also credit your name in the description. Thank you.
Ok then you have to wait for an hour and a half and I don't need any credits
Chain effect 👍👍😁
Jesus loves you ❤️ please turn to him and repent before it's too late. The end times described in the Bible are already happening in the world.
@@L17_8 bro is on drugs
I have a question. Suppose a(n) is the integer sequence A007916. Does the series (1 to inf) 1/ (A007916(n))^2 conv or div?
Please next videos:24 indefinite integrals and
24 definite integrals
(High level problems)
And happy teachers day
The amount of care you take that the viewer really gets it and doesn't trip over a step you are making is absolutely amazing
Thank you!
I watch these while eating because I dont know what Video to watch
I dont comment often but i felt that i should mention how helpful and entertaining with me learning calculus and other math. Also i loved this video
Thank you!
@@blackpenredpenHey I am taking AP precalculus, we are over hallways through unit 2 and it doesn't seem too bad. any suggestions on how to master my algebra (especially algebra 2) skills that are lacking from having those classes over zoom. Thank you 🙏
42:20 still watching, doing the questions and watching your explanation if I get stuck. Thank you for all your great videos!
Hi backpenredpen!!! You always keep me motivated to record math videos!!! Sometimes I ask myself why should I continue making math videos on youtube, but then I watch one of your videos and they inspire myself to do it!!!🤗🤗🤗
What is that reference board you are using and where can I get it? Great video!
Love you sir....❤️❤️❤️
From india
We aren't studying Trigonometry..
But i understood all you taught....
On the 14th question i think we can simplify it to
Cos(x)Cos(2x)=2Cos³(x)-Cos(x)
Its heartbreaking to see the expression being not factorised... 🤣🤣
Any way..
Big fan sir
You are wonderful...🔥🔥❤️❤️
(And Happy teacher's day also❤️)
Thank you so much. This will help a lot in my calculus studies. 🙂
Glad to hear that!
Could you please make a video on jee advanced maths section
Happy Teacher's Day Love from India ❤ 🇮🇳
nice!
you are the goat, i was struggling with this topic then you popped into my recommended list and now im decent at it, thank you
Glad to hear 😃
Idk why I always feel satisfied when he erased the whiteboard 😂
Please do 100 differential equations I need them for my exams😭😭
yesss that would be super helpful😁
Jesus loves you ❤️ please turn to him and repent before it's too late. The end times described in the Bible are already happening in the world.
12 th m h kya bhai
Thanks prof i really learned a bunch of things
42:39 I could watch a movie of these
Thanks!!!
24 Trig Problems done in *one* take, that's gotta be BPRP, aka 'The Beast'. Identity mathematics presented the way we spoilt brats have grown used to. Don't take this man for granted, though!
Jesus loves you ❤️ please turn to him and repent before it's too late. The end times described in the Bible are already happening in the world.
My interest in mathematics has grown so much because of you. You make so good content. Huge fan of your work. Thank you so much.
I pick up a lot of small details in these longer videos!
Glad to help!
Thanks BpRp
you're one of the great maths teacher 😎🖤❤
Q13: I had 1/[(sin^2(x))(cos^2(x))]=4/[2(sin(x))(cos(x))]^2=4/[sin(2x)]^2= 4csc^2(2x). Would this be considered a correct answer?
I love your videos, keep up the amazing content!!! Btw, I'm in Precalculus learning Trig Identities!
Q14: cosx*cos2x=cosx*(2cos^2(x)-1)=2cos^3(x)-cos(x) Is this OK?
Setting 2cos^3(x)-cos(x)=1/2(cos(x)+cos(3x) ==> cos(3x)=4cos^3(x)-3cos(x)
for q6 an alternative solution would be to take the -1 as being equal to -sin^2(x)-cos^2(x) (multiplying original identity by -1) and substituting, then simplifying the equation down to sin^2(x)
really helpful video, i love all your tutorials
Intro - 00:00
1 - 00:51 - sinx+cotxcosx
2 - 04:40 - (secx-cosx)/sinx
3 - 07:16 - cotx/(cscx-sinx)
4 - 09:00 - (1+2cosx)/(2+secx)
5 - 10:45 - 1/(1-sinx)+1/(1+sinx)
6 - 13:00 - (2+cot²x)/csc²x-1
7 - 15:36 - tan(x+π/4)
8 - 19:11 - cos(3x)
9 - 24:09 - cos(4x)
10 - 29:32 - sec(sin^-1x)
11 - 32:42 - cos(2tan^-1x)
12 - 36:56 - tan(2sin^-1x)
13 - 42:44 - csc²x+sec²x
14 - 45:41 - cosx cos(2x)
15 - 49:38 - sin⁴x
16 - 57:22 - sin⁴x-cos⁴x
17 - 1:02:04 - tanx+tany
18 - 1:04:47 - 2tanx/(1+tan²x)
19 - 1:07:25 - 1/(secx-1)+1/(secx+1)
20 - 1:12:08 - (sinx+tanx)/(1+cos(-x))
21 - 1:16:14 - cos²x-sin⁴x sec²x
22 - 1:14:50 - (sinx+cosx)²
23 - 1:20:18 - sinx/(1-cotx)+cosx/(1+tanx)
24 - 1:23:57 - sec²(x/2)
Thank you so much!
Happy Teacher's day Sir. Today 5th September every year in India we celebrate Teacher's Day to so our love toward the teachers. Your lecture are just brilliant i following your channel since 2020.thak you sir for everything.
I would love it if you’d do some extra identities for the parabolic version of trig fies. So cosp and sinp identities! Why? Cause they behave somewhat different than the normal sin/cos and hyperbolic sinh/cosh versions!
Love you sir ❤❤❤❤
Thank you so much for this amazing video
Cool thing to note:
8cos⁴(x) - 8cos²(x) + 1 = 8sin⁴(x) - 8sin²(x) + 1
Digamma(x)=1
Solve this please, it's too hard
Or explain digamma (x)=y , find x
I didn't skip a whole 10 min ad 😂😂 hope this counts for you, because i don't have money to send
7:30 lemme just take a look at the camera (nope he is definitely taking a look at the solution jk)
Do all the 24 identities you did but hyperbolic trig instead
my comment down below at the 42:39 time stamp ⏯
1:03:31 Easy, cancel cos from both sides
I lose sleep over these videos, even though I may or may not know the content😅
I now prefer to stay home and do calculus on my weekends
Plz solve Integral of log base 2(x*(sin2ex))
these were very easy as I am in high school
Master of it ❤
Where do I find the identities board?
Happy teacher's day sir🎉
can you do inequalities please
art
Awesome job!
Calc 2 savior
Challenge:- solve 100 ordinary differential equations in one go,,,,next 100 partial differential equations in one go
broo ❤❤
42:40 yes, doing it with you. I've also done the 100 derivatives twice now, and the 100 algebra twice, too... Great practice!
42:40 yes i am following along solving all the questions, they're pretty easy, excited for the upcoming questions
I don't understand why he puts cos3x = (cosx)(cos2x)..This seems wrong, because for example, cos 60 = o.5, but cos 20 is .9397 and cos 40 is .766, and multiplying these these gives an answer of of .7198. which is nowhere near .5 ! Can someone please explain? I Thanks
Hey David! He didn't put cos 3x = (cosx) (cos2x) instead what he did was simply write the 3x as 2x + x. cos(3x) = cos(2x + x)
Thanks for answering. I now see that what he wrote was (cos x)(cos2x- minus (sin x)(sin 2x). Silly me !! @@AttyPatty3
Further to mt previous reply, can you please tell me if there is any way available to derive the formula cos (A + B) = cos A.cos B - sin A.sin B ?@@AttyPatty3
My Lord!!! Thank you very much!!! You had simplified my life!! I’m back in school after many years, and I was struggling into I found your video!!!
Where did you got the T-shirt and the table you have on the wall???
I appreciate your time, dedication and advice!!!
18:55
This is driving me crazy i wanna cry so bad
you can do it my friend
I have a question. Suppose a(n) is the integer sequence A007916. Does the series (1 to inf) 1/ (A007916(n))^2 conv or div?
I'm taking AP Precalculus this year and so far its not bad. So far its just been obtaining a deeper understanding of functions and what values can be obtained from the equation of a function.
Hello!! I've just finished watching 50 integrals video, and I'm so happy to see this as I'm struggling with trigonometry!
thank u for this. i took ap calculus bc and skipped calc 1 and 2, and im scared of trig identities coming up in chapter 12 for calculus 3 !! big fan
Do a 100 question One Shot version and put in 100 question playlist
Is ex. 2 an identity? Because in the original fraction all values equal to kxpi are not in the domain.
7 can be simplified to tan(2x)+sec(2x)
and 13 can be 4sec^2(2x)
hey whats that black identity board you have hanging beside the whiteboard? is it available online?
😂Imagine, sir, that you unplug the camera lol
His smile just makes me wanna study more
Do more integral battles between elementary and non-elementary ones! The one you did 4 years ago wasn’t enough for me.
This video was VERY helpful, thank you!!
I have an equation who solves it 13:19
Hey man you are really an inspiration for me.your passion keeps me motivated ❤
Do inverse trig identities next!