Trigonometry made easy
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- Опубліковано 15 жов 2019
- Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. In this video we look at the use of trigonometry with right triangles, solving for both sides and angles.
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BTW for those interested - the history of trigonometry history is fascinating!
The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.
The use of trigonometry really took off due to it's use in navigation - trigonometry has been used for locating latitudes and longitudes of sailing vessels, plotting courses, and calculating distances during navigation.
Trigonometry is still used in navigation through such means as the Global Positioning System and artificial intelligence for autonomous vehicles.
But the truly cool trigonomic endevour was The Great Trigonomical Survey.
The Great Trigonometrical Survey was a project which aimed to measure the entire Indian subcontinent with scientific precision. It was begun in 1802 and completed of it in 1871.
Among the many accomplishments of the survey was measurement of the height of the Himalayan giants: Everest, K2, and Kanchenjunga. The Survey had an enormous scientific impact as well, being responsible for one of the first accurate measurements of a section of an arc of longitude.
Triangulation surveys were based on a few carefully measured baselines and a series of angles. The initial baseline was measured with great care, since the accuracy of the subsequent survey was critically dependent upon it. Various corrections were applied, principally temperature. An especially accurate folding chain was used, laid on horizontal tables, all shaded from the sun and with a constant tension. The early surveys made use of large and bulky theodolites made by William Carey, a Zenith sector made by Jesse Ramsden and 100-foot (30 m) chains!
Interesting aside - Everest was one of the leaders of the survey - and his name was pronounced Eve-rest not Ever-est! To donate to the tecmath channel: paypal.me/tecmath?locale.x=en_AU To donate to the tecmath channel: paypal.me/tecmath?locale.x=en_AU
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Never thought Thor will be teaching me math.
Well that was dry 🌵
@@Change685 like my sense of humor 😎
@@thepillow13e39 😎
@Destructo WIZ 😎
@@vinnypixel6460 😎
Thanks a lot sir
Learned more concepts in minutes than in hours in school
Yep
As much as you hate it, you don’t need to talk trash about something to complement someone
@@helplure yeah it is, but I just don’t like people mixing some negativity with a compliment
@@babz527 bruh shut up
@@charwtsn he’s right tho. School is undoubtedly the most inefficient place to learn but you don’t need to be that hateful.
I'm 31 years old now and going back to get my diploma(which we call dogwood here in Canada). Your videos have helped me immensely, the teachers that I have and text books aren't clear enough but you certainly make it clear. I really appreciate that you made this, thank you from the bottom of the heart.
Joe mama
@@mad.j0j070 lol
@@mad.j0j070 that was soo random 😂🤣
im 15 years old and have my GCSEs over here in the UK, its a lot for a kid to learn imo.
So… you want dogwood? Hmmmmmmmmmm
i’ve been trying to do trig homework for literally 4 hours and you are by far the only person who’s been able to actually
make sense thank u sir
guts doing math?
@@selkirkr3x it was my version of the eclipse
short, to the point, helpful, and easy to understand. I have a test today due at midnight and my teacher is incompetent. thank you for teaching me this in 12 minutes what he couldn't in 4 classes
Wow! Cool.
Test due at midnight?!
@@sissi9100might have been an online test
@@sissi9100Covid was probably still lingering
These videos have helped me to help my son, who sits his GCSE exams starting tomorrow. Thanks so much for such a great way of teaching all of these subjects. There really is no reason for parents to shy away from helping their kids with such great help and the manner in which you teach these really does aid learning.
hope your son does well!
@@Jamie567 Thanks, results in August but he was at least happy going into the exams that he understood what was being asked of him.
@@davidbentley4099 I'm taking the gcses in 2 years time roughly if covid doesn't mess the system up
@@Jamie567 Good luck, get ahead on revision and keep focused.
@@davidbentley4099 so how did your son do, did he pass the exam?
10:06 if your using a Casio calculator its shift then press on sin ( and for 6:07 it is 6.84 not 6.88)
Yea I got confused
he probably rounded
Math way says it’s 6.88
Just because of rounding
Thank u I got confused
anyone here day before their test?
Me
Nope, I'm here 3 hours before the exam
@@brunamilicevic7151 gl brother
I've got 6 hours 😭😭
Yup
Awsome! I understand this topic better in 12 minutes than 1 1/2 hours a day in class.
Facts
@@EvanGoddock Sorry for disturbing you but could you explain why sin35 equals 0.57, tan48 = 1.11, and . Do sine, cosine, and tangent have values? Also, what is the need for sin^-1?
@@neelrama5938 just pop the formula in a calculator
Something like Sin(35 and then you equals
@@neelrama5938 it’s because you want to find what sin(35°) is so you need a calculator to find that
If you use your calculator and say sin(35°) it will tell you it’s 0.57 and the same goes for tan(48°) it’s 1,11
There is a button for sin, cos, tan
Yes sin, cos, tan have a value
Sin^-1 is used for finding angle degree just like the first one you asked about sin(35°), tan(48°) etc
I hope this helps you to give a better understanding of trigonometry :-)
@@neelrama5938 you don't need to know why tbh, it'll always be on the Calculator Paper just pop SIN(35) into the calculator
After completing this video I agree that trigonometry is one of the most feared topics in mathematics. I learned that trigonometry only works on right angled triangles. I learned that the length of the sides are named (a, b, c) due to its respectively opposite angle. I memorized the 3 equations as SOHCAHTOA. Allow me to demonstrate it: Sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse and tangent equals opposite over adjacent. Sine= SIN, Cosine = Cos and Tangent = Tan.. As I was watching this video the lesson became easier and easier. You are already provided with 1 angle which is 90 degrees and more information will be given to complete it. All you have to do is place the numbers in the right place according to the equations and simplify them to get your results. Your final answers may turn out in decimal numbers. Don't freak out, just continue and don't overthink it. If your teacher allows the use of calculators, you will be able to do it on it. However, only use the calculator to make sure of your answers or if huge numbers are given. I honestly thought I would have numerous questions to ask. However, I watched various videos before this one. The way you explained it was phenomenal. Great Job!!!!!
memorizing SOHCAHTOA isnt a really good way of understanding the sin, cos and tan functions. I'll give you a better more geometric interpretation of these functions. So, if you take any point A, on the unit circle, (circle with a radius of a unit, in the cartesian plane)draw a line to that point and the origin, (0,0), and draw a perpendicular to the X axis, and then join that point on the axis back to the origin, you get a right angled triangle. The line you just drew to the X axis is the sine function! Isn't that cool? The math is pretty simple, since sin = opp/hypt, the hypt will always be 1 as its the radius of the original circle so it will always be just the opposite side. Similarly, the compliment function to the sine, aka cosine or cos is the line you drew from the point on the x axis and the origin. Same math. The tangent function is the point you get by drawing a *tangent* to that unit circle at that point A (yes, thats where the tan function gets its name). The segment you get by taking the distance to that tangent segment and the X axis gives you the tan function, and the segment you get by joining the tangent to the Y axis gives you the compliment of that tan function, aka cotangent or the cot function. So just by using pythagoras' theorem you can derive the ratios on the spot, without ever needing to memorize it
Also, if youre interested in calculating any value of sin(x) without knowing the opposite or the hypotenuse, there is a very beautiful series, called the taylor series. According to this series, the value of sin(x) = (x^1/1!) - (x^3/3!) + (x^5/5!) - (x^7/7!) + (x^9/9!) and so on forever. Truncate at any point, and you get a veryy good approximation of sin(x). This is also btw what calculators use to compute the value. similarly, cos(x) is the same as sin of x, except it has every other even number, instead of the odd number pattern of sin(x)
If you dont believe ill solve an example out by computing the sine of 1
as i said
sin(x) = (x^1/1!) - (x^3/3!) + (x^5/5!) - (x^7/7!) + (x^9/9!) so therefore
sin(1) = (1^1/1!) - (1^3/3!) + (1^5/5!) - (1^7/7!) + (1^9/9!) (and i chose one cause powers of 1 are easy to compute)
sin(1) = 1/1 - 1/6 + 1/120 - 1/5040 + 1/326880
sin(1) = 1 - 0.16667 + 0.00833 - 0.00019 + 0.000003
= 0.83333 + 0.008311 + 0.000003
= 0.841664 which is a very good approximation of sin(1). (actual value being ~0.8414)
Trigonometry is easy there is no need for a video to prove that
Thank you
@@Jamilah.L you're welcome
This is the most helpful trigonometry lesson. It was very easy to follow along. Thank you
l know 😭
True
Ppp
Even though I knew this already I really appreciate the great videos. Also I love that I wasn't the only one who wrote simpler equations to get the order right!
Oh yessssssss babbbbyyyy
i do that too! I do it in tests and my teacher always puts a ton of question marks next to it like wtf are you doing lol
Why did this not make sense at school. I've learned so much in a few minutes😃
So true!!! Videos like this save lives:-)
@@SeaWisdomtv yes, in 3d application
You can make very fluid animations with expressions, for example, snake can move in S curve shape in repeating cycle all thanks to sine function.
i swear its your voice , but the way you teach math doesnt make me want to cry . Absolute legend , thank you.
Love it! I'm in school right now and they just dropped a sneaky little trig class out of nowhere, I'm sweating bullets, this is a great video, I wouldn't mind seeing more of these just for repetition, all the other videos from others just confuse me, well done to you sir
You tube brings the great teachers of the world to the masses. Your lectures are brilliant !
I got excited at the "friendly equation" to the side, I had no idea other people did that! got me through loads of chemistry, glad you're spreading the word about it:)
Thanks for this. It was so easy to understand, I even showed 3 of my friends this video because they were struggling in class. Now they understand it because of this video
my brain is not braining
Righhht 😭
Bruh I’m in 6th grade and this is ez
Jesus christ, I've spent hours on one assignment, wandered off to this video and completed the assignment in less than 10min. You're a lifesaver, mate!
If you can get this and most of this channel's content, you would definitely know more than most high schoolers
We learn this in middleschool tho
Wow thank you! Your explanation was great. I feel like I actually understand how all the concepts work together now.
Thank you so much mate. I'm 32 and going back into schooling to finish off my electrical apprenticeship. You've given me a huge relief with this video. Extremely simple to understand.
This has got to be the best Trigonometry video ever for learning, my teacher wasn’t able to explain the concept to where I could grasp it but now watching your video I got the concept immediately, Thank you.
I couldn't understand any of this until I watched your' video, thank you very much! You were very descriptive and explanatory about how to work everything out.
you just saved my life, I have the PSAT on Wednesday and I've never done trigonometry ever and all the videos expected you to have background knowledge except this one. Thank you so much!!!!
Same lol he is a lifesaver
My class has recently started dying trigonometry, and I had been having a hard time with it, and the teacher hadn’t explained in in the best way, but now I can do it! I’ll still definitely need to refer back to this video, but it’s been a great help.
Thank you for your time! I'm 5 years out of high school and starting college this year so these kinds of resources are invaluable to me.
absolutely amazing! i have my actual GCSE exams in around 6-7 weeks (give or take) and i never really got the gist of trig until now that is. Thank you for making this video this has helped me and others! also that little trick with rearranging the the numbers- ill be sure to use that as that was always the bit i got stuck on so thanks for that as well! :)
super close now! hope you succeed in all areas :D
@@rubenchacko3444 Thank you very much! all im aiming for is to get even a small pass like a 4, a pass is a pass for me! again thank you 😁
@@livinglifeo4509 hasn't exams started? they did in my school, hope you're doing great!
Hello sir. Thank you. I was struggling with trigonometry,and now I can remember all of it.
Bro you are a genius. I'm stuggling with 9th grade trigonometry and spent about 1 hour reading through the texbook and when i looked at this video i realised how easy it is. It took me minutes to understand it compared to the hours i was wasting. Appreciate this video. It helped me a lot
I have been through countless videos and none of them explained it better than this one thank you so much you have saved my life
Honestly, simple trig is one of my favorite parts of math. From the unit circle to LOS and LOC it’s great.
Mate I'm 40 ans about to start an engineering degree at UNISA and can tell going to be watching alot of your videos, keep up the good work you are a good instructor especially for Aussies, no offence to the Indians but you're heaps easier to listen to
This is amazing, I’ve got a test on trig on Friday and this has helped massively thanks
My son needed help with trig for schoolwork. This is helping me learn it faster than any other math channel. Thank you!
I will be patron soon. I need to learn curves and more today.
Hello! I really enjoy watching your videos! I understand them so much thanks!!
0:00 introduction
0:14 basics
3:44 sin
6:27 tan
8:29 sin
10:39 cos
12:00 ending
8:29 *actually sin
Thank you. Clear and friendly. Voice tone is so important; sometimes videos have super scientific and rushed narratives. Your friendly voice helped me to concentrate on the facts.
I watched other videos and I couldn’t really understand them, I luckily stumbled upon your video, it was short, VERY easy to understand, taught me a few extra tricks and your voice is extremely nice and calmly thank you for the amazing video.
Hello, this was an amazing and short tutorial on an explanation of trigonometry and it was very easy to follow. Thank you for making this amazing kind of content, and you are truly helping a lot of us out here. You just taught a complete seventh-grader how to do trigonometry lol
Doing trig soon in class so I wanted to read up on it before hand BC it sounded confusing when others explained it. This was way easier to understand
I have been in so many classes and done so many problems that have had this involved and iv never understand it but this video reallyyyy helped my out. From the bottom of my heart thank you
Thank You, for you're informative videos Sir! I'm a beginner to Trignometry, as I am in 9th now... in 12 mins I have understood and have got a basic understanding of what is trignometry and how do I use it... Thank you once again sir!!
You know the school system has failed when u learn more in 12 mins than a whole 2 hour lesson
English isn’t my first language so it was kinda hard to understand but I pretty sure I get how I’m supposed to do it! Thank you for this video! Keep up the good work
What’s your first language
Thank you so much. My teacher is lovely but explains things to me way too quickly. Your videos have been a huge huge huge help. I feel much more confident. Bless your heart for making this.
Thank you so much for this tutorial, I'm currently less than 8 hours away from a maths test, and this just saved my life!
Way to break it down into a very understandable video. Thank you!
The Voice, the colors, the visuals, will all help me to get a 100 on my test. Thank you.
you just saved me from failing thank you so much. I've been sick and missed all my classes and my finals are due in two days. i was completely lost and this just saved my entire year thank you so much
You have a God given talent for teaching. Thank you for your patient and detailed approach and cheers.
Bro taught me maths in under 20 mins while my teacher had been struggling for three hours. Just proves it's a skill issue.
@@Isa-sj9sy lmao what 😭😭
@@robo0o what did they say if u remember
I LOVE soh cah toa. As a kid, I remember how easy it was to remember. I would visualize some university students chanting it in Greek life for some reason, lol. It helped. It’s such a great way to memorize a formula.
This guy is actually making sense unlike those cringe-ass music videos.
Thank you so much! I have been struggling with this for days and I finaly understand it!
My daughter was struggling with this topic because she had a bad MathTeacher. Lucky she found this video which was well explained and the tip 3 =6/2 was extremely helpful.
Edit : Just wanted to say big thank you.
Thanks for helping me for my first year of high school in geometry
Thank you! I have been working and haven't had time for in class tutoring. This was exactly what I needed
Wow best explanation of trig, I’ve come across UA-cam so far, simple easy to follow examples,thanks so much
Thanks! Really well explained! You have a good calm pace for those of us who are new to/rusty on the topic. As an 'old hag' my students only have to think of me to remember the mnemonic :) I like your 'friendly equation' too ! ... Tip for slow learners like me - set playback speed to 0.75 - it still sounds quite normal, but just gives a bit extra brain processing time!
Thx for the playback speed tip
Thank you so much, this was better than my 1hour class!
Bruh. I thought it was super complicated didn’t know it was that easy. My teacher had to of course complicate everything. Thank you very Much for helping.
Thank you so much sir! I literally understood this lesson in a couple of minutes instead of hours in class! That was really helpful ✨
Crazy how a 12 minutes long video made me understand trigonometry more than hours and hours of school
Fr
SO HELPFUL!!
thanks sm, im in my second semester of college and my prof just assumed all us students would understand this so he didn’t explain it at all but now im finally starting to get it because of ur vid, keep it up!
Brilliantly explained video. I understand how this all works now and you taught it better than my university lecturer.
Silly old harry Caught a haddock Trawling off Australia. That’s what we were told
I was told silly old Hitler couldn't advance his troops over Africa 😂
@@tom-ez1np This Hitler one is easier to remember, but I don't like giving props for Hitler.
The highest respect to this man, he þaught me what no teacher did.
You are awesome. I’m completely taxing my children your methods. Makes it way more simple to understand and get correct answers!
Great video. I've been out of school for over 20 years and found myself trying remember what tan^-1 stood for. You're video was a great refresher for somebody like me.
Thank you for the video sir
This really saved me
I have a trigonometry test in 2 days and it's really gonna help me
How did it go?
@@sahilpatel0701 I can't even remember but I'm pretty sure I passed that test
@@dhruvkore1324 ok nice 👍
I like this video but it seems trigonometry is ultimately 'How to use your calculator.' Any chance of a run through without a calculator including all basics needed to work it out the old fashioned way? Cheers.
same thought! it would be great without the use of a calculator, to get a better understanding.
Very helpful basic explanation, which was all I wanted. Thank you.
Very simplified! Thank you so much! I've been pulling my hair out at work trying to figure this out! Now I get it!
great vid got an assessment tomorrow!
gl
W to all those who dident listen in class and decided to just search it up
Pov im in grade 11th and have 20/100 grade in math 10c
Thank you so much for this. I struggle to learn math at school because of my autism and trigonometry has had me in a choke-hold all this time. But this video helped me so much; I'm getting the hang of it. I may not know it fully but this has done wonders keep up the good work.
Honestly I’m in grade 7 and my final math exam is tomorrow, I didnt understand trigonometry fully until I watched the channel. This guy is the best😊
This video is simply INCREDIBLE, thank you!!
Thanks . I always remembered soh can toa but never knew how to apply it to a right side triangle. I guess I missed that class when my teacher showed it. Anyway I am now 48 years old and came across your video
How simple. I can't beleive not one teacher couldn't see i was struggling with this and could not explain it like you just did.
Thank you
Soh cah* toa. Although I'm going to assume that's autocorrect's doing
@@tristanhofer2491 lol yes the beautiful auto correct. Thanks
Thanks so much for posting this.
Trying to help my son with his exams, but it's been 40 years since I did trig and it hasn't been easy remembering it, but thanks to this video I am at one with it again.
I've just just started trigonometry in maths and after 1 hour of my teacher trying to explain it to me and not understanding it , your method made me understand it all , thank you so much
I'm doing mechanical engineering just started never thought it would be so heavy with maths
Engineering seems like something that would require quite a lot of math
Is it not more physics based than maths
@@Anonymous_56789 it's both and they put them in long confusing questions
Hey Mate,
Thanks for the wonderful explanation, just wondering if you could have any practice worksheets related to this?
Thanks
I know im a month late, but just look up trig practice worksheets and theres literally endless amounts, be specific with what u search tho so u get precisely what you want.
@@TheNineNations where did u find them?
@@GlizzyGobler9000 try khan academy
Thank you very much. I'm a 25 year old guy and I needed to know how to find an angle's number for a personal project.
I've studied these things when I was in high school but never understood them until today.
THANK YOU!!! I was rlly struggling w this topic and you helped me a lot
can you kindly explain how you got 0.57.
If you enter sin(35) into a calculator, you will get 0.57 as a result
i hope you get 100 lottery tickets and win all of them
love this vid was really struggling because i couldnt understand the way my teacher was teaching me and this really helped.
In my 37 years...i never knew how beautiful this was. I never gave trigonometry a chance. it sounded scary to me. but...this is beautiful! i like how you can see the math and the relations. this is literally eye opening. now i understand how a person can tell how tall a building is just with an angle.
also....this means that rectangles are really two right triangles kissing hypothenuse. so you can do some fun stuff with other shapes as well.
then if you need to measure that rectangle...you can split it into one triangle...and just measure that and BAM since the other triangle is a mirror reflection...whatever you do to one you did to the other. lets say you need to find the center point of side A. the opposite triangle has a side identical to A as well. so you can make a cut on A and then a cut on the other A and its the same. you dont have to measure again (if it is a perfect rectangle).
that means...if you need to break a rectangles parameter into 8 equal parts...you can break it into two triangles first....then focus on breaking one triangle into 4 equal distant parts.....and you basically found the 4 on the mirror reflection of that. you found 8 equal distances of a rectangle without having to measure the entire thing out. i need more math! honestly never noticed how important and beautiful and mysterious it can be.
If a person did not use a calculator, what is the formula from cos to get the degree of the angle?
If x is your cosine value, the angle is approximatly (180*(π/2 - x - x³/6 - 3x⁵/40 - 15x⁷/336))/π degrees
@@HakanTheUltimateHoca In other words, good luck not using your calculator
This was so clear and helpful. My only request is that it would be nice to see what the equation would look like in the calculator when using the inverse of sin cos or tan. Like 0.71 cos^-1
Yeah, on my calculator it came up as 45.1 degrees only when I put in cos(-1) 0.705 not 0.71. How would you know when to round and when not to round?
i like the way you explain it, you say pointless things to fill up a little bit of time so its an easier pace to absorb the information, very good thumbs up 👍
30 years thinking I must just be a bit dim and all it took was you to say think of it as 3=6/2. anyone who gives you hate can go enjoy themselves. thank you very much for this.
How do you get 45.1 in the last problem? 🤔
ikr I got 44.8
@@skdab0297 I got 44.7 I’m so confused 😩
Should be 44.7
In a test I had one of the questions goes something like this:
/P PQ is 60% longer than RQ
/ | Work out the length of RQ.
/ |
R/___|Q
It mentioned something about using sine as well but I’m not sure in what context.
I’m not sure if this is exactly how the question goes but if anyone know what I mean and can help me for tomorrow I would really appreciate it!!
Hey! PQ=1.6xRQ and Pythagoras theorem applied: PR^2=(1.6xRQ)^2+RQ^2, ^2 means squared. Hence, RQ=PRxsqrt(1/3.56)=0.53PR
MATH SCIENCE by Daniel Dallas thank you so so so much! Honestly I really appreciate it💗
@@mollyiscool5008 No problem. Ask questions and I will try to help U
@@DANIELDALLAS_MATHs Curious why you put Sqrt(1/3.56) instead of Sqrt(3.56)??? You seem to have gotten the wrong answer.
Woah, like thank you. Was never taught trig very well but this, this changes everything.
Love your trigonometry video it’s helped me understand trigonometry better thank you