Trigonometry Lessons Part 1: Definitions

[@jamilachowdhury7278]

What a wonderful video.... no body taught me like this when i was a student... I am now a doctor and reside in Dhaka, Bangladesh.... but i watch maths video to recommend to my son (who is now in year 8) and also to learn myself. I showed this video to my son..... he liked it so much! Thank you Jane, You are great.

[@janepianotutorials]

Hello Dr. Jamil, enjoyed your comment. Thank you for writing. For some of us, it is always fun to look at math. Glad your son is motivated, and hope he does well. Best, Jane

[@janepianotutorials]

Update May 2023, responded to a comment today and discovered that I had not replied to many comments (lack of time). Thanks to those who wrote 9 or more years ago. Hope all of you did well and have careers that you enjoy.

[@janepianotutorials]

@Rachel Rose Estrebilla Google+ will not allow me to REPLY to your comment. The sohcahtoh scheme is terrible. Forget about that completely. Then watch this lesson from the beginning. Pause and rewind when you do not understand anything. The definition of tangent as sine/cosine is most important. When the triangle sides are used, it comes out as adjacent/opposite.

[@janepianotutorials]

To all, I started to edit the automatically generated YT closed caption today. What a mess they made of it. It'll take me a few days to finish. Those who requested subtitles in Portuguese will be able to use the translation feature.

[@kazisahid9728]

Thank you mam

[@janepianotutorials]

@Ishant Bibaan your comments do not have a reply option. extra work to reply :( can I ignore you from now on? :) my first language was not french

[@janepianotutorials]

Got busy doing other math topics. Might do more high school trig next because of your comment.

[@janepianotutorials]

@Claybear17 the values come from the triangles in the examples

[@WooshaBaloo]

I'm confused. You teach Maths AND Piano??

[@janepianotutorials]

+WooshaBaloo I'm always confused :) But math is my major, piano is my hobby

[@janepianotutorials]

easiest way is to use my website. there is a "math tutorials" page that lists the ones I've done. log and exp belong in precalc. I'll get to those someday, perhaps sooner because you asked.

[@janepianotutorials]

in layman terms, a function assigns to each input value, a unique output. as you saw, a trig function assigns a number to each angular measure. there are other functions that have to do with triangles, such as inverse functions. functions are useful. without functions there will be no advanced math. you can read more on wikipedia. math is FUN :)

[@janepianotutorials]

to distinguish among various concepts, such as angles and sides, or different coordinate systems.

[@janepianotutorials]

Added subtitles in English. The tool setting allows translations. Hope that helps!

[@THEGANJASAINT]

+Jane WHERE R U FROM JANE?

[@THEGANJASAINT]

+Jane WHERE R U FROM JANE?

[@janepianotutorials]

a few continents. most of it in the U.S.

[@THEGANJASAINT]

are u married?

[@janepianotutorials]

read about me on my awesome (lol) website? click my name to get there

[@janepianotutorials]

uploaded part 1 on sine function examples. part 2 will be on the cosine, and include changing periods.

[@janepianotutorials]

not sure what college algebra consists of, because algebra i and II used to be in high school. this belongs in high school trig.

[@janepianotutorials]

@stevalianarbone amazing that the casio battery still works. i used to use a slide-rule! you probably never heard of those :)

[@janepianotutorials]

@Banvoolivre your request for a piano tutorial does not belong here :)

[@janepianotutorials]

no need to be sorry, just rewind and review until you understand all of it. this is a very important basic lesson. you need to understand every bit of it to do well in math later.

[@janepianotutorials]

@MrPianist101 one lesson will not be of much help because algebra encompasses many topics. I did one on factoring that you might find useful in Algebra II. The best thing you can do is get a Barron Algebra thick workbook (library) and do as many problems as you can. my husband and I are seriously considering starting a math series, but you will be way ahead of us by then. good luck. algebra is fun, and it is an important foundation for calculus. you can message me questions any time.

[@janepianotutorials]

there are thousands of math topics, hard to choose from... will keep your suggestions in mind.

[@janepianotutorials]

was that necessary?

[@janepianotutorials]

most learn that as part of calculus. will add to list. all six functions?

[@janepianotutorials]

You're very welcome. Thanks for writing, and I hope you do well in your upcoming trig course.

[@janepianotutorials]

it is not a "demo"

[@janepianotutorials]

meaning of the name of each trig ratio? please explain.

[@janepianotutorials]

please review your square roots. those fractions are equal.

[@ruixxxx]

I burst into tears finding this video of yours, Ms. Jane. I wish I could've attended your class in high school and college. Math and calculus exams still remain so regular in my nightmares. Thank you for your both math and piano tutorials, enjoyed and learned. The cheat sheet in the final is a gem.

[@janepianotutorials]

Oh Ruixiong, so glad you found this trig lesson and it helped. Take your time to learn, understand everything before moving on, then you will enjoy math and do GREAT! Be happy 😊

[@janepianotutorials]

why was this in algebra? trig is fun and easy. get a good work book, study one section at a time and do the problems. if you have questions, send them to me and I'll help you.

[@janepianotutorials]

If your background is strong, i.e., if you really know your algebra, geometry, and pre-calculus, you’re going to do well in college calculus. You don’t need a high school calculus course. The above was the conclusion of a long-term Harvard research study, published July 2018. It's upsetting and incredible that something so obvious was ignored for the last 50+ years.

[@janepianotutorials]

@paper900 mutation?

[@janepianotutorials]

how did you do? :)

[@janepianotutorials]

glad to know that :) keep at it and have fun. you're welcome to send me questions.

[@janepianotutorials]

that is simple algebra. should be automatic like 1 + 1 before one learns trig.

[@janepianotutorials]

sq rt (2^2 - 1^2) =sq rt ( 4 - 1) = sq rt (3)

[@janepianotutorials]

how would you handle a roomful of unruly teens? is that what your teacher is dealing with? luckily I never had to deal with such problems.

[@StevePhillips]

I been working on your Trigonometry demo today Jane, and though seemingly easy to follow, from looking at your tabe I got to brush up on my fraction devisions. I wrote it all down as well as you mentioned in another video to do. It does help. I also used my casio scientific calculator fx-82A to find square root. (I bought it back in 1988 and still battery is not run out and is working perfectly.

[@janepianotutorials]

please do not use vulgar language to comment under my videos, even if it is meant to be complimentary. if math is _____ in your country, you can learn on your own. khan academy covers almost every topic.

[@janepianotutorials]

sorry for my late reply. algebra is a pre-req for trig

[@janepianotutorials]

lol, you are the first one who commented on my joke. I had thought my lesson went down the drain.

[@janepianotutorials]

Bach minuet in g

[@janepianotutorials]

hello @Ishant Bibaan, you're welcome :)

[@bradleyhewitt4885]

Jane just wanted to know, at 2:48 how is it an equilateral triangle. Isn't it an isosceles? Feedback will be much appreciated.

[@janepianotutorials]

Hello Bradley, hope the following makes it clear: Definition. A triangle with 3 equal sides is called an equilateral triangle. Definition. A triangle with 2, and only 2, equal sides is called an isosceles triangle.

[@bradleyhewitt4885]

Thanks for the help Jane!

[@janepianotutorials]

Bradley Hewitt Glad to help, Bradley!

[@janepianotutorials]

the hypotenuse is always the longest leg. look at the picture.

[@janepianotutorials]

please do not confuse my students. this is high school trig. they have not learned about 'functions' yet.

[@alexanderkrizel6187]

I'm confused. at 6:15, you say cos45=1/sqrt2. In the table at 11:15, cos45=sqrt2/2. ?????

[@janepianotutorials]

Those are EQUAL. I made a video to address your question! see video description

[@alexanderkrizel6187]

Hello. Thank you for the reply and thank you SO MUCH for the videos. Yes, I saw they were really the same thing when I went back and looked closer. Is there a reason to write them different in the table? You posted a video about it, so I will go back and watch it. Thank you again for the videos. I have always regretted not taking more math. Now that I am old enough to understand how big a mistake that was, I have decided to go for it. Your videos are a huge help. Thanks so much.

[@janepianotutorials]

Alexander Krizel I Alexander, a new comment brought me back here. Yes, I made all the denominators 2 to make the chart easy to remember! See the pattern in the numerators?

[@janepianotutorials]

You're welcome Waldor. Glad it helped.

[@brianmclogan]

keep up the hard work!

[@janepianotutorials]

finding a good trig textbook appears difficult. I've been searching the library without success.

[@janepianotutorials]

you're very welcome. happy to hear the good news :)

[@raminaklove877]

Jane, Thank you so much for refreshing my memories from the school after almost 20 years. I really enjoyed listening to your lecture. I just felt as If I were a young student and was sitting in the class. Please keep up the good work. I would love to check out your website, too. Once again, Awesome Job. I loved it.

[@janepianotutorials]

+raminak love nice to hear from you. glad you find enjoyment revisiting trig. it is amazing how a simple idea as taking ratios of sides would lead to vast applications.

[@janepianotutorials]

thanks for writing, Yash :)

[@mcw0805]

can you make a video on graphing trig functions with shifts, amps, etc.?

[@janepianotutorials]

don't know what to choose. plenty of word problems already... want trig ids?

[@ettabrown3880]

This is an awesome tutorial because it teaches the basics in a simple, yet gentle, format within a few minutes that anyone can understand! Everybody can't teach, this video proves that Jane can!!!!! Kudos :)

[@janepianotutorials]

+Etta Brown Thanks for your kind message, Etta:)

[@janepianotutorials]

@SuperOutcast55 very funny, at least now you see why I don't say anything on piano tutorials :)

[@raykrv6a]

Hi Jane. I found this Trig lesson fun as I'm 63 years old and brings back memories. I remember writing all the formulas down and using a slide rule to build the answer. Calculators make it too easy in my opinion. I actually found you on KZbin because I bought a Yamaha Digital piano and starting learning. Thanks for all the vids. Math is fun.

[@janepianotutorials]

raykrv6a Nice to hear from you. People our age were fortunate to learn trig before that SAHCAHTOA mnemonic became the *standard* way of introducing trig. Mnemonics promote memorization with zero understanding. There goes all the fun! Teachers, especially math teachers, must avoid using mnemonics. Congratulations on your new piano and new hobby. It is a wonderful one. Hope you started with my sight-reading lessons.

[@janepianotutorials]

Good to hear from you. Best of luck on your entrance exam. If you are interested in how basic trig can be applied, see word problems. I recommend PatrickJMT.

[@thenextmarlon]

Thanks Jane, have an entrance exam next month for MBA. Knew nothing about trig, you helped me a lot. Cheers and keep up the good work. :)

[@janepianotutorials]

Great, you must have earned your MBA by now 😊

[@janepianotutorials]

you're welcome. glad it helps.

[@ThinkOutside07]

thank u very much, is there other parts? Have you videos about log and exponential function? I was searching for that on your page, but there is too much piano videos, it doesnt make it easy to find out what you are searching for. Pls distribute videos by subject on your page. I wish I found your videos earlier, really helpfull, thx again. (sorry for errors)

[@r08y]

Thank you for this. I was about to jump back into trig as a non traditional student and was feeling a bit anxious about starting math again. This seemed to put me a bit at ease.

[@allanfisch]

I had not seen or heard this for 35 years. Thank you. And thank you for the sight reading lessons that I am now going to check out.

[@janepianotutorials]

Have fun with the review! Hope the reading lessons are useful.

[@50southern]

love part one of your trig.video i learned what I couldn't learn back in high school in the 70's. Thank You; Now is it possible that you could upload a part two of trig? and maybe if you could add ratio proportions,percents,fractions,basic shape measurements and how to an essay? Thank You: Billy

[@THE16THPHANTOM]

oh lord where do i find the second one i need more. every video i've seen so far stops here like this one and trigonometry is never spoken of again.

[@janepianotutorials]

glad to help. and thanks for the compliment :)

[@MrPianist101]

Is there anyway you could do an Algebra Lesson for me? I'm going into algebra next year for my sophmore year. Thanks!

[@MONGTRAN11]

I would like to ask the music song from beginning.Thanks a lot.

[@LILNAPPIHEAD]

This is fantastic! Can you post more videos please.

[@lsefia]

I totally love your video, brought back memories, unfortunately I didn't get as good an explanation as you did now back in the day, but I have the privilege of passing your video on to my kids. Thanks!!!

[@josephwonderless1258]

Jane is there a site on you tube where I can learn Trig from the beginning? I had Pre Algebra, Algebra 1 and 2, and College Algebra, a long time ago. Around the year 2000 in a community college. And I would like to learn trig from the beginning. Thank You.

[@janepianotutorials]

I haven’t looked at trig lessons since I made mine. Have you checked? Avoid any who teaches by acronyms. Acronyms take away from understanding. Have you considered self-learning from a trig book?

[@eugenecedricngoreyes]

What was the music at the start of the video? It seems very familiar.

[@janepianotutorials]

eugene reyes Bach / Petzold Minuet in G Major :)

[@sammariofan]

Is this class harder than college algebra? or vice versa? any reply would be greatly appreciated

[@amilabdullayev2702]

9:15 nice break when call of nature cannot be put off

[@janepianotutorials]

+Amil Abdullayev that was meant both as a joke and a _test_. most videos are watched less than 2 minutes. it took more than one year before some viewer commented on that flush! :)

[@amilabdullayev2702]

+Jane Well I pity those who didn't survive up to the flush moment ;)

[@janepianotutorials]

@AreWeStillFree1 I am not familiar with trig textbooks. will ask a local HS teacher or you. for calculus, I strongly recommend author Howard Anton. let's correspond via personal messages after this.

[@janepianotutorials]

yes

[@janepianotutorials]

purportedly 32 yrs old from Australia? are you proud of yourself for announcing your adversity to math?

[@glenncupido2311]

THANKS!!!!!!!! Couldn't have passed my Trigo test without this vids

[@janepianotutorials]

@jinxler disappointed? :)

[@ziracornelius83]

Thank you for this video, I'm trying to familiarize myself with Trigonometry before taking it during the short winter session since my work prevented me from taking it in Fall, I've looked at other videos and the slow instruction really helped the information "sink in", (pausing the video helped too) Much appreciated!

[@GneissBiscuits]

How do i figure out whether to use sine, cosine, or tangent?

[@janepianotutorials]

Draw a right triangle to start the problem. Fill in what's given. And put a question mark on what we want to find.

[@kazisahid9728]

the basic formula means All the sin cos theta etc but what IS THE sin 45 = 1 by root 2 and by the way which Language you spoke

[@janepianotutorials]

Not sure what you mean. There are subtitles in English. You can translate to your native language with the cc tool.

[@spencerwhite3400]

And, How is theta defined? You said it was THE angle, which is pretty hard to figure out for something called a TRIangle. Is it the angle the hypotenuse and base make?

[@janepianotutorials]

Over-thinking! We are simply giving the angle in the picture a name so we can talk about it. Greek alphabets are commonly assigned to angles in calculus.

[@MrStationb]

i could never figure out when to use cos or sin and this is the only video that CLEEEEAAAAARLLLLYYYYYYYYY EXPLains it...thank you for being very detailed...

[@janepianotutorials]

excellent, but please don't call your teachers stupid, okay?

[@gudikandulasurekha7194]

Nice explanation

[@janepianotutorials]

Thanks again

[@tobefree8510]

I love Trigonometry :) I studied it alone years ago... And found it simply amazing !!! Good job as usual !!! I think that I'll follow your courses just because you speak slowly, and that will help me to master the mathematics vocabulary and syntax in English :)

[@janepianotutorials]

Daniel, surprised to find you here. Glad you are making use of these lessons. Enjoy...

[@tobefree8510]

Yes, they are great lessons, helping my English :)

[@SuperOutcast55]

tho if i can't fliping understand your esths language, how can i understand Pythagoraths therom?

[@janepianotutorials]

That's nice. I wish you smooth learning.

[@sammariofan]

college alg is like alg 2 but with more information. it's also offered as a high school course just like trig. but i have to take them again in college since they werent worth college credit

[@geocarlacavalcante5561]

please make videos with subtitles in Portuguese

[@janepianotutorials]

Oh my, any volunteers?

[@Finkanslig]

@ 11:08: Learn the sin θ line; flip it for the cos θ line. Do tan θ = sin θ / cos θ for the last line. :I:

[@janepianotutorials]

Finkanslig think I said that too. "flip it" sounds like a reciprocal though :)

[@johnnybee1776]

Nice job explaining everything. You spoke nice and slow so the information had time to process in my rather small brain. I learned more in lesson one and two than I did in four years of high school. Some people speak geek and like to speed thru everything to show how smart they are but they are poor teachers. Again nice job people loke me appreciate it. Thank You

[@janepianotutorials]

Whoever came up with that 'sohcahtoa' acronym (memorizing without understanding) messed up several generations of math students.

[@sandhyasandhya612]

there is a mistake in it sin45 degrees is 1/root2

[@janepianotutorials]

you are wrong dear! ace your algebra before doing trig. in video description, I provide a link to the lesson that 1/(rt 2) =( rt 2)/ 2

[@janepianotutorials]

glad it helped Brandon. trig is FUN! :)

[@janepianotutorials]

you're welcome

[@ほエ]

I haven't take trigonometry yet so... What do you find out by figuring out the sin???

[@janepianotutorials]

+Boltofvolt acoustics, architecture, astronomy, cartography, civil engineering, geophysics, crystallography, electrical engineering, electronics, land surveying and geodesy, many physical sciences, mechanical engineering, machining, medical imaging , number theory, oceanography, optics, pharmacology, probability theory, seismology, statistics, and visual perception (from wikipedia, applications of trigonometry)

[@ほエ]

+Jane I meant what do you find out about that triangle by doing the sin?

[@janepianotutorials]

+Boltofvolt the sine in a triangle tells us the ratio of the triangle's opposite side divided by the hypotenuse. that is all. but as we learn more math, the sine develops into a wave function

[@janepianotutorials]

pay attention everyone: for all my math tutorials, take out pencil and paper and work on the examples with me. takes notes as if you were in a classroom. have to involve as many brain cells as possible.

[@100of1000]

I belive You are proffesional teacher. You are also great speaker/announcer - helpful to learning english.

[@janepianotutorials]

glad it help. have fun with trig :)

[@meko2420]

hey....at 3:22 my answer was 1 but when i added instead of subtracting i got 3

[@chrisleyraymond9212]

Is this the right answer for the math home work from your first lesson the hypotenuse is equal to 61??

[@janepianotutorials]

chrisley maximin Can you do it for the 3,4,5 triangle? Here the two sides are 24 and 7. Find the hypotenuse once more? The answer is given in the next panel after the homework problem at @12:43.

[@jordanblythe104]

Im using the fx-82B