Trigonometry Basics
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- Опубліковано 6 сер 2024
- Trigonometry Basics : LIVE Class at 8 PM Today!
Introduction of Trigonometry will be discussed in a simple way!
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Q). *In a right angle triangle, if A = 90° and tanC = √3 then find sinB cosC + cosB sin C*
Sol:
*Method1:*
tanC = √3 = tan60°
⇒C = 60°
We know that A + B + C = 180°
⇒90° + B + 60° = 180°
⇒B = 30°
∴ *sinB cosC + cosB sinC*
= sin30° cos60° + cos30° sin60°
= (1/2)(1/2) + (√3/2)(√3/2)
= 1/4 + 3/4
*= 1*
*Method2:*
*sinB cosC + cosB sinC*
= sin(B+C)
= sin(180°-A)
= sinA
= sin90°
*= 1*
This guys is single handedly better than my entire school with 50 teachers
I'm watchin this video in 2024😂
Same just now, I'm preparing for exam
Same am preparing for a exam tomorrow😢. Hope mi pass😭😭
@@ShackeriaDavis-ne6ue
Good luck ❤️
Good luck👍
Same here 😢
The answer is ....
Tan C = √3
By trigonometric table,
tan = √3, then C = 60°
By angle sum property,
∠a + ∠b + ∠c = 180°
90° + ∠b + 60° = 180° ; 150° + ∠b = 180°
∠b = 180° - 150° ; ∠b = 30°
By trigonometric table,
Sin B = Sin (30°) = ½
Cos B = Cos (30°) = √3/2
Sin C = Sin (60°) = √3/2
Cos C = Cos (60°) = ½
Sin B x Cos C = ½ x ½ = ¼
Cos B x Sin C = √3/2 x √3/2 = ¾
From the equation,
Sin B Cos C + Cos B Sin C = ¼ + ¾ = 4/4 = 1.
So the answer to this equation is 1.
I have a doubt...
Can we also solve this equation like this ↓?
From equation,
Sin B Cos C + Cos B Sin C
By rearranging,
Sin (B+C) + Cos (B+C) = Sin (30º + 60º) + Cos (30º + 60º)
= Sin (90º) + Cos (90º)
By trigonometric table,
Sin (90º) = 1
Cos (90º) = 0
From the factorization,
Sin (90º) + Cos (90º) = 1 + 0 = 1
@@user-sj6hy8ze8c
sinB cosC + cosB sinC
= sin(B+C) + cos(B+C)
*This is wrong.*
*Formula:* sin(A+B) = sinA cosB + cosB sinA
∴ *sinB cosC + cosB sinC*
= sin(B+C) *This is correct.*
= sin(180°-A)
= sinA
= sin90°
*= 1*
Not Gonna Lie but MANOCHA ACADEMY IS BETTER THAN BYJU'S
Thanks a lot :)
true af
Really
Yes
Absolutely right.
Playlist containing set of 4 long lectures on Trigonometry: ua-cam.com/play/PLn6POeOJkCuLVwh6RLfFDx0WnMhHocE0a.html
52 minutes and 25 seconds of pure master piece
sir i am in 9th std , and i had the curiosity to learn the basics of trigonometry, and my wish is now fulfilled only because of you sir, thank you sir
you are in 9th me in 7th
I'm in 6th
I think the answer for the homework question is 1, as tan 60 is √3/1. The hypotenuse will be 2 when calculated by Pythagoras theorem. Therefore, sin B=1/2 and B is 30. cos C=1/2 and sinBcosC is 1/4. cosB is √3/2 and sinC is √3/2 and cosBsinC is √3/2 * √3/2 = √9/4 = 3/4. When they are added 1/4+3/4= 4/4=1, so the answer for the question must be 1..
It's even more easier as we learned in school to call those formulas with sides, adjacent, etc... but here with calling it as perpendicular and hypotenuse like p/h, b/h, p/b makes it more easier than that type
Spending 52 minutes for this video is valuable, very very valuable....
And also Sir, I like your way of teaching.
Glad to hear that
Thanks a lot sir for the explanation, i can picture a paper where i have already got everything correct
Most welcome
Most Welcome
@@ManochaAcademy sir the answer is 1 isn't?
Hi 🤴🤴 king 👋😘😍😍😍❤️😍
@@pushpdahiya3044 ilove you
Can we call Base and Perpendicular as Opposite and Adjacent??
My maths teacher taught us like that!!
you could, you can even denote those by random letters
This Guy is saving my tution fee.........
😄😄😄
Me too
Even my physics sir shows ur videos in online classes...... I m not at all joking..
Same here
Here too
Ya
Same here :"))
ua-cam.com/video/e52IviFBBr8/v-deo.html
sir....ur the only one teaching in english...most of the teachers take in hindi..i cant understand...im from tamilnadu....tq soo much for taking the class in english
You are most welcome
For guys who don't understand
I explained you have seen protractor which is shaped like D
We use D to draw angle we draw 90°angle which is called right angle a right angle have 3 side hypotenuse adjacent and opposite the diagnol line is hypotenuse right to it is opposite and left is adjacent
When you take length of adjacent and make it square the make square with opposite side which number is given is given then you got square of hypotenuse in math it is called Pythagoras theorem a²+b²=c²
Adjacent is 3cm opposite is 4cm
Then according to Pythagoras theorem 3 square is 9 and 4 square is 16 and a²+b²=c²
9+16=25 and √25=5 length of hypotenuse is 5 cm
For tommorow's exam u helped me a lot sir thank you very much
All the best
9th guys dont take trigonometry lightly if you want to acquire Engineering and other technical studies ahead .....i did take it lightly in my school days that time i was good at it but then i started taking it more lightly ...and now 21 yr old me watching it back right from beginning 🥲🥲🥲
❤From Kerala
I am 10 class
while seeing this lesson in textbook is like🤯but when I listened ur class it’s looking easy and I gained confidence thank you sir🥰
Yup same looks way harder than it actually is
Hi sir! Hope you're doing great! My maths teacher had shared a memorandum with our class to help us remember the ratios of cos, sin and tan! I thought it would be easier for ppl to remember these ratios thru it, hence I would like to share it if you don't mind!
It goes like this:
𝙎ome 𝙋eople 𝙃ave,
𝘾urly 𝘽lack 𝙃air
𝙏hrough 𝙋roper 𝘽rushing.
The letters in bold refer to cos, sin and tan, whereas P, B & H refer to Perpendicular, Base & Hypotenuse respectively. Hope it helps! Also thank you for the wonderful video sir!
Nice mnemonic!! Thanks for sharing 😊
@@ManochaAcademy My pleasure sir! The credit goes to my maths teacher!
@BLACK SEVOU credit goes to my maths teacher!
Thanks for sharing
By the way are you BTS army?
You are one of the best teacher in the world sir, thank you for your support
Wow, thanks
Very good explanation sir @@ManochaAcademy
I am only 4 years late
nope
🎉
Words are not enough to thank you Sir . Please keep on uploading new videos.You're a life saver.
Hi, I thank manocha academy for all. I'm a student but not in India and I'm in a secondary school. I was asking about the inverses in trigonometry. How do the work? Cause I have not heard about them.
how ab=bc? are we taking specify the type triangle to understand the tan 0 value?
I think that using the “base” and “perpendicular “ is confusing when work with a different angle. 50 years ago when I learned trigonometry we used “side opposite to angle” and “side close to angle”
I told to my friends to listen to your classes when I was listening in pandemic you helped us a lot you are much better than our school teachers .
After watching lot of videos I came across your one. Very detailed and beautiful teaching. You are best than my teacher at school😅
if i have teachers like you in my 12th i may be in different position ... thank you sir... i finally learned trigonometry ...thank you so much... and the answer is 1.
is it easy?
because im having problems too
What if the value of theta is given is it required for answering
if it helps please like... for sin cos and tan theta if someone is using adjascent opposite and hypotenuse an easy way to remember this is Old Henry for O/H (opposite by hypotenuse for sin theta), And His for cos theta Old aunt for tan theta so the sentence formed will be Old Henry And His Old Aunt
thank you for making our maths much more easier
Happy to help!
Thank you for making the english language much more stupider.
@@TennesseeZ i don't blame you
Sir we can write the base as adjacent wholesaler and the perpendicular as opposite right
Respected sir...what instruments and software ,you are using to make these videos....please tell me
I am in 9th but wanted to learn this trigonometry before my 10th. Now thinking why students are afraid of this chapter? I don't think so it's too hard to understand... By the way you explained it very well sir. Thank you..!!🤓🙃
Your lessons are absolutely amazing... I love it the way you make it interesting.
I have a doubt can we say that "sin" is inversely proportional to "cosec " because you have written it as sin = 1/cosec
the answer for the home work question is 1\4 + 3/4 which is 4/4 i.e the final answer is 1
It was a prestigious explanation.
Thanks sir I don't have sufficient words for praising you.
I'm in class 7th, my bro said trigonometry is hard i just came to check it out and damn it is hard💀
And I'm in 8th,but found it easy anyways 🤷, your brother is in which class?
@@bhatadha9255 I'm in 8th now too but I still find it hard lmao, u must be very good in maths, btw he's in 12th now
I love how he teaches us from his heart. Really appreciated sir. Thanks Alot!
How an angle is defined?
For better Iq, for better education, for better qualification join manocha academy👍🏻
Thanks for liking
Sir i am in class 8th and i am interested in learning trigonometry from now and these are good videos given by you 🙂👍
For me it's more like I NEED to learn it for physics 😭
AND I AM IN CLASS 7 🙂😂
I have never ever found such a great teacher like u sir, the way sir teaching is one of my my favourite teaching type it makes me to understand very well
Sir, when do we use this type of sin, cos etc...??
Sir, the answer is 1 , here are the steps, angle b=30 degree, angle c=60 degree, 1/2×1/2+√3/2×√3/2=1/4+3/4, =4/4 that's 1
Perfect answer
Super! Right answer :)
Who u find angle b pls tell me
Angle b=30
Thank you so much sir. You make it simple and relevant. Keep it up.
Excellent teaching!! Thanks for this great video.
This is so helpful, all my basic concepts of trigonometry are clear..😁.. I've been looking for a video with such great explanation.... thanks a lot!
Sir please conduct a live session for this year students pls.. not a day passes by without ur video I want u to conduct another live
Will soon do
@@ManochaAcademy thankyou sir
Thank you sir for giving these kind of excellent explanation. I understood very clearly
Glad to hear that
Can I ask about the last sum,that how u took that identities when it is given that tita is30
sir could you please use the table and show it ( in the last question) as I have tried I couldn't do it....
The answer to the HW question is 1.
Excellent!! Right answer!
Yes sir plzz do make a video on iit maths class 9 syllabus
Very understandable 😊.. thank you for this..
Very good teaching easily understandable. Well done 👍👍
i never understood trigonometry in school and tutions but somehow i understood by watching this video?😭 thank you
I have my exam tmw and ur my life saviour thank you so much sir 💜
how did you do
Happy to help
@@xoxodelphiI did great 😃 this video was much helpful to me .
I wish you was in sky school Hargeisa Somaliland. And teachers like you are the most needed types of teachers for the world
Thanks sir you helped me a lot I am learning basic for physics work power energy (resolution of vector)👍
u are a genius sir . never have i understoood trig that easy anywhere.
Hey sir it's helping me for my cycle test for my term 1
This so good I started trigo tday and got the hang of it
Thx for superb explaination
Thanks for teaching sir,I understood better than school teaching. Thanks You are teaching best sir thank you sir.
😘😘 thanks beta 🤗
When you will keep again live sir
Real video starts from 1:31
The best maths teacher ive ever seen on UA-cam, God bless you sir
So that makes it two angles right?
Q
A=90°, B=30⁰, C=60⁰
= SinB (1/2) x cosC (1/2) + cosB (√3/2) x sinC (√3/2)
= 1/4+3/4
= 4/4
= 1
Answer 1
Yes😄
There is a unique way of teaching in you sir.Thank you .even the tips for the exams are very useful for all of us.🎊🎊
Most welcome
i wish I had a teacher like you in my school days
Sir you really explain very well......
Thank you for the explanation of this chapter
Thanks for the explanation sir, your explanation is very awesome
You are most welcome
Sir app ki tara koi dunia mah education nahi dae sakta ☺☺
Thanks a lot. Share with your friends
ua-cam.com/video/TesMy8kDun4/v-deo.html
Dekho
Find the values of x between 0° and 360° satisfying the equation, 10sin²x+10sinxcosx-cos²x=2.
10Sin²x + 10SinxCosx - Cos²x = 2
⇒10Tan²xCos²x + 10TanxCos²x - Cos²x = 2
⇒Cos²x(10Tan²x + 10Tanx -1) = 2
⇒10Tan²x + 10Tanx -1 = 2(1/Cos²x)
⇒10Tan²x + 10Tanx -1 = 2(Cos²x + Sin²x) / Cos²x
⇒10Tan²x + 10Tanx - 1 = 2(1 + Tan²x)
⇒8Tan²x + 10Tanx - 3 = 0
⇒8Tan²x + 12Tanx - 2Tanx - 3 = 0
⇒4Tanx(2Tanx + 3) - 1(2Tanx + 3) = 0
⇒4Tanx - 1 = 0 or 2Tanx + 3 = 0
⇒Tanx = 1/4 or Tanx = -3/2
⇒x = Tan⁻¹(1/4) or x = Tan⁻¹(-3/2) = - Tan⁻¹(3/2)
∴ *x = Tan⁻¹(1/4) + n * 180°* or
*-Tan⁻¹(3/2) + n * 180° where n ∈ Z*
Given x between 0° and 360°,
x = Tan⁻¹(1/4)+ 0° or
-Tan⁻¹(3/2) + 180° or
Tan⁻¹(1/4) + 180° or
-Tan⁻¹(3/2) + 360°
∴ *x = 14.036°* or *123.69°* or *194.036°* or *303.69°*
Superb explanation sir you made us understand in a very short period of time in a easy way
Sir thankyou so much tommorow is my exam and now I am preparing for boards and I found the best vdo ever 😊😊😊
All the best.
aye same, sed bros.
There is a simple trick for learning formulas of trigonometric Ratios i.e OLD HARY AND HIS OLD AUNT and sir this video is really Amazing. You are a good teacher.
Explain please!!!
@@avinashlokare5744SIN THETHA= OLD HARRY:- OPPOSITE UPON HYPOTENUSE, COS THETA= AND HIS:- ADJACENT UPON HYPOTENUSE, TAN THETA =OLD AUNT:- OPPOSITE UPON HYPOTENUSE
@@darshantomar953
Thanks😊👌🏿
Sir ,30:35 there how are you getting 0°, 1/2, 1/√2etc..
Sir this was truly inspiring
It was soo up to the point
Ur the best teacher that I have seen so far
U made it seem so easy
Hats off Sir !
Thank you so much sir ! Your help means a lot to me and you definitely deserve a sub !
Thank you, sir
Tomorrow is my maths quiz, and though I am still 7th I understood everything you thought. You teach very well.
Trigonometry at 7th grade?
Trig in 7th dam bro
What is the answer of final question.......?I got the answer 1;is it correct sir?
Thanks!!! It really hekped me for my math week in school!
Welcome!
Sir..U r teaching is very good...I am understanding very well..tq sir
Most welcome
For everyone Who Did Not Understand 3 Square + 4 Square = 9 + 16 = 25 root Of 25 Is 5 and thats how we got five as Hyp
Ohhh godddd thank youuu so muvhhh !!!
That is h²= p²+b²
Thank you i was struggling with this concept and you made it easy for me
Given,sinA=5/13
From the following ratio,
Perpendicular=5x
Or, Hypotenuse=13x
Or,(13x)^2=(5x)^2+b^2
Or,169x^2-25x^2=b^2
Or,144x^2=b^2
Or,b=√144x^2=12x
We know,sinA/cosA=tanA
Or,(5x/13x)x(13x/12x)=5x/12x=5/12=tanA
Thank you so much for sharing this sir 😊❤️ it's really very usefull ✨
U are the best online live classes on youtube,im a class 5 student but your explanation is so good that i understand all u said
Glad to hear that
Same😊
sir how to find the heigth of a leaning tower it wont be 90 right
I prefer your videos to my classmates that they can understand easily, in every subject that you explaining method is very easy sir
Thank you so much sir for making this helpful video for every student of class 10th 😊
Most welcome
Not only 10th students of 9th and 11th also
Your explanation with your fluent language ....is best 😊😊
yes
Sir you are great I was thinking this lesson was too Hard but you make it too simple ❤️❤️❤️
What a wonderful teaching sir please become. Maths teacher and be teaching maths