Common man you're making a video about solving trigonometric equations and the best question you're doing is sinx=1/2? Next it's gonna be 2+2. Make extra easy questions so people understand easily and have them feel like you're the greatest teacher so they watch all your other videos and pay for your classes, got it 👍 Oh jeez the second question actually is cox=-√2/2 😂😂
I'm still completely lost. Trigonometry so far just seems like "Now this equals that because as it is a common fact that all circles with the angle equal this and applying our trigonometric identities it just works."
At this point, it just takes obedience. Just do what you're told until you get your degree. Apparently, it doesn't start making sense until late Calc II.
@@user-ov9vo3ku9y I haven’t fully watched the video yet, and I’m fairly stuck too, but most of the time understanding how to get the answer comes from memorizing the unit circle
Dude you have saved me so many times. Every time my textbook gets confusing, I can always find a video you have on the concept. Thank you for taking the time to make these wonderful videos, and making this knowledge free to everyone.
meh u need to remeber 3 numbers and ur all good, 1/2, root 3/2, and root2/2 and if u think about it visually the rest are the same they just add a 2/3/4 or something infront
@@joeljose7159 yes bro picture the unit circle in your head, and remember 1/2, root3/2 and root2/2 and know which angles correspond to which values, which is memorizing
@@Nikblor Literally every single answer here can be found by applying a reverse radian formula on the reference angle you discover through the 45/45/90 or 30/60/90 triangles; TLDR: You don't need the unit circle (besides the base 3 values of COS, which are reverse for the SIN, and SIN/COS for TAN)
i memorized the first quadrant and it's super helpful. then finding the other quadrants if I really need them on a test is easy, i just draw a little reference unit circle
trigonometry is the most gut wrenching nail biting skin tearing eye watering foot cramping brain malfunctioning shit to ever exist for me in mathematics but you have just saved me. I am willing to sell you both of my kidneys just for saving my dumbass. Thank you.
I'm coming to the end of my academic year and you've been so helpful throughout this year.🤧 I don't think I could have managed without your help. Thank you so much and I pray God gives you whatever your heart desires.❤
Mr. Organic Chemistry Tutor, thank you for solving Trigonometric Equations and Finding All Solutions. This is where I have some problems with trigonometry.
one thing that has helped me out through my calculus classes when i forgot decomposition, was the quadratic formula, they both are able to line up at some point so it kindof gave me another option
Brooo i just spent 3 hours trying to understand this from the videos my teacher posted in MS teams... and u explained it in 10 minutes...wth..can't you teach my teacher???
How do you just 'know' that an angle of 135 and 225 are 3pi/4 and 5pi/4 respectively? Where is the chart that says that because I am very confused as to how this works Also at 10:34, how do you get the fraction values in terms of pi withot knowing sin x first. If it was left as +-1/sqrt 2 that is just sin 45 onn the reference triangle. But there is no triangle that lets you do sqrt2/2 or -sqrt2/2, so where do you get the angle that translates into e.g pi/4?
co terminal angles. These are the angles that will be in the exact location no matter what is their angle. For instances, 30 degrees is just the same as 390 degrees but both going to a different direction. I think he was just trying to imply that whenever we add 2pi to the value it will just be the same
You're The most intelligent teacher ever ,never stop teaching i appreciate you so much i am new for your channel i think I'm doing great thanks. one thing i wanna say is believe in God and the son(Jesus ) b/c God created us for his purpose ,this world will be passed one day I'm from Ethiopia (🇪🇹) don't forget the coming of the lord
I'm still not understanding how you get 5pi over 6 inthe first problem. You would take the sine inverse of 1/2 to get the answer and it has a restricted domain of negative pi over 6 to positive pi over 6. Youre doing the same thing in another video. I just dont get how theres an inverse rule of which quadrant the answer is from and how you get 5pi over 6 that goes past the domain boundary. Please explain to me. I would really like some answers to my questions on both of your videos
Graph the equation (sinX) then type in y=K(y=1/2 in th3 first example) Then the first two times the graph crosses the line y=1/2 are the 2 (main) solutions. :) Also: to get the second cosine, make the x negative and add 2pi, or after add 1 period to get the value of both cosines.
OH RIGHT I forgot they have different periods. In class they just started giving solutions with no explanation, and I had to figure out what the hell they were doing. I figured out the unit circle bit, but didn't understand why some answers were adding different multiples of pi.
You don't have to memorise it. You can just use the trigonometric triangle - search it up. Very easy to draw. Just need to remember the lengths of each side (1, 2, and root 3) and you can quickly sketch it out/refer to it whenever you need to find an angle.
@0:08 what is the value of x ..... and then @0:19 you know the answer... how on earth did you solve this??? it is supposed to be algebric calculation or formula or equation... If we already know the x, why are you asking to solve it??? lets say you have sin x = 240... how do you find x?? do you use logarithm? e ?
This is a bit late (about a year, apparently) but yes, you are correct. That's because in this problem the solutions are 180 degrees apart so the periodicity is pi (or 180 degrees) and the answer is as you state above.
Because Of coterminal Angles. He was trying to imply that 13 pi/6 has the same as 5 pi/6 because the problem states that we must find all the solution therefore, we must add 2pi into 5 pi/6 as they will just result into the same value
n can be any integer (-2, -1, 0, 1, 2, etc). Whenever you add 2pi *n to the original angle, you can think of this like doing one revolution around the unit circle (which is 2pi units long) and you end up in the same location, and the sin/cos or their inverse will give the same value.
Dude is it me or is anybody else super confused. No offense to this dude cos I've watched so many vids and am still lost. This was probably the most clear but I'm still confused.
can we talk about how my boi had negative square root of 3 /divided by 3 and then just disregarded the numerator when he drew the triangle? talking bout some 1, 2, and square root of 3? Like...what? where the heck did 1 and 2 come from??
π is in there, because radians are used a lot in Trigonometry. I would say if you’re taking Trigonometry right now.. really study the preliminary concepts like the unit circle. When you get really good from degrees to radians… this will all make sense to you. π/6 is 30 degrees. 5π/6 is 120 degrees. π is 180 degrees, etc and so forth.
pi*n is for tan/cot, since their value repeat every time the angle increases by pi (you can look at their graphs, notice how the shapes repeat every pi amount on the x-axis). For every other trig function, you add 2pi*n to the answer.
So to find all solutions we have to add 360n but in my book some questions have answers such as 180n can someone please explain to me why my final exam is tomorrow and im so confused on this topic :,)
You probably figure this out by now, but I will leave this here for people who need help. if you have a solution like π/4 and 5π/4, they are π distance apart from unit circle. so you can condense the answer to π/4 + πn. if you plug in 1 to n you will get 5π/4.
@@SM-qn7sr Thank you! I was taught this but it has been a couple of years since I have done trig. This cleared the example at 8:00 up. I appreciate it!
Brother may Allah give you bad luck. It’s 1 AM, test is in T-Minus 7 hours I have been watching this video for 2 hours and haven’t understood a thing. What rhymes with booked, cooked of course I am cooked good night now. Leaving this in allahs hands and JPs bund crack.
There is literally no need for all of this you don’t need to think about the angles that will give you the same answer. We have formulas for sin cos and tan that will give you immediately the two options in terms of n
I think some people need to know both. My teacher is making us use both. I have a quiz on this tomorrow and she even said that it will be bother degrees and radians. maybe he could have done it better in the video, but it is good to know both.
Trigonometry - Free Formula Sheet: bit.ly/47diggI
Trigonometry Video Lessons: www.video-tutor.net/trigonometric-identities.html
Common man you're making a video about solving trigonometric equations and the best question you're doing is sinx=1/2? Next it's gonna be 2+2. Make extra easy questions so people understand easily and have them feel like you're the greatest teacher so they watch all your other videos and pay for your classes, got it 👍
Oh jeez the second question actually is cox=-√2/2 😂😂
I'm still completely lost. Trigonometry so far just seems like "Now this equals that because as it is a common fact that all circles with the angle equal this and applying our trigonometric identities it just works."
Same, I can't get it in my head I just don't understand how he gets the answers. RIP.
I feel like everyone have different methods its confusing. I can even get why some have 2 on pie n and some have not 🤕
At this point, it just takes obedience. Just do what you're told until you get your degree.
Apparently, it doesn't start making sense until late Calc II.
@@user-ov9vo3ku9y I haven’t fully watched the video yet, and I’m fairly stuck too, but most of the time understanding how to get the answer comes from memorizing the unit circle
he is basing the answer by having a reference to the unit circle
Not all heroes wear capes. Some do math. You my friend are a hero!
Bro ty in literally just trying
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Dude you have saved me so many times. Every time my textbook gets confusing, I can always find a video you have on the concept. Thank you for taking the time to make these wonderful videos, and making this knowledge free to everyone.
Bro graduated since he commented
Of course you felt this was easy he was doing sinx=1/2 lol
For anybody having issues: you need to memorize the unit circle first
meh u need to remeber 3 numbers and ur all good, 1/2, root 3/2, and root2/2 and if u think about it visually the rest are the same they just add a 2/3/4 or something infront
@@joeljose7159 yes bro picture the unit circle in your head, and remember 1/2, root3/2 and root2/2 and know which angles correspond to which values, which is memorizing
@@Nikblor Literally every single answer here can be found by applying a reverse radian formula on the reference angle you discover through the 45/45/90 or 30/60/90 triangles; TLDR: You don't need the unit circle (besides the base 3 values of COS, which are reverse for the SIN, and SIN/COS for TAN)
i memorized the first quadrant and it's super helpful. then finding the other quadrants if I really need them on a test is easy, i just draw a little reference unit circle
@@joeljose7159 yeah that kinda is what the unit circle is...
trigonometry is the most gut wrenching nail biting skin tearing eye watering foot cramping brain malfunctioning shit to ever exist for me in mathematics but you have just saved me. I am willing to sell you both of my kidneys just for saving my dumbass. Thank you.
LOL no need to sell anything.. this was free
Beautiful. I have a feeling my teacher won’t teach this before act, so I am happy to have such a straightforward teacher on yt.
That last example was pure gold man! Thanks!
God bless you you’re such a savior
Idk if it’s just me but I have forgotten everything from the start of my trig clas
Yea same here. Since our teacher began discussing trig class, my mind totally went blank.
you're not the only one
More than any other chapter for some reason
somehow i can still derive the unit circle and its been like 3 months since i have taken trig
Coming back here after I've graduated. This channel saved my ass before math exams so many times lol.
Good, but I would like you to solve more difficult problems....
İ love your way teaching
You are the greatest teacher i have ever seen
İ am from syria and your videos helped me alot
Thank you so much for explaining everything in such detail! You’re a life saver
I'm coming to the end of my academic year and you've been so helpful throughout this year.🤧 I don't think I could have managed without your help.
Thank you so much and I pray God gives you whatever your heart desires.❤
Mr. Organic Chemistry Tutor, thank you for solving Trigonometric Equations and Finding All Solutions. This is where I have some problems with trigonometry.
Just had my mind blown 3 times, this guy is amazing at teaching.
Not me watching this in the middle of my math quiz because I didn't listen to any of the lessons
Why is scaramouche watching the organic chemistry tutor
I've sought refuge in this channel so many times after my professor fails to teach good and just has us referring to the textbook
Thank you for saving my math grade ☺️
one thing that has helped me out through my calculus classes when i forgot decomposition, was the quadratic formula, they both are able to line up at some point so it kindof gave me another option
I have been beating myself up not being able to fully grasp this. God bless you.
Very good, but you need to increase the volume of your mic
This is really gonna help for my organic chemistry test tomorrow.
I learned it as +2kpi. That is the same thing right? Also, your channel is a life saver.
Yeah it's the same only difference is your "k" value is his "n" value
This man is a blessing to mankind 👏
Excellent. I just have to remind my students to explicitly say that n is an integer in their solution. Thank you!
Name me even one practical application in the real world that you would even need trigonometry or calculus?
Brooo i just spent 3 hours trying to understand this from the videos my teacher posted in MS teams... and u explained it in 10 minutes...wth..can't you teach my teacher???
channel name = chemistry
video type=maths
teaching skills =einstein ++
im convinced that im incapable of learning
literally thank you so much
How do you just 'know' that an angle of 135 and 225 are 3pi/4 and 5pi/4 respectively?
Where is the chart that says that because I am very confused as to how this works
Also at 10:34, how do you get the fraction values in terms of pi withot knowing sin x first. If it was left as +-1/sqrt 2 that is just sin 45 onn the reference triangle. But there is no triangle that lets you do sqrt2/2 or -sqrt2/2, so where do you get the angle that translates into e.g pi/4?
memorize the unit circle
0:25 where does the five come from
Trig table sin(pi/6)=sin(30°)=1/2 and sin(5pi/6)=sin(150°) which is also equal to = 1/2
very helpful
thank u
When would we use 2pi(n) and just pi(n)?
tangent and cotangent are pi the rest is 2pi
You are a legend god bless you
Still dont get it. How did you add 2pi to pi/6
co terminal angles. These are the angles that will be in the exact location no matter what is their angle. For instances, 30 degrees is just the same as 390 degrees but both going to a different direction. I think he was just trying to imply that whenever we add 2pi to the value it will just be the same
thank you so much i get it now
Where is the 5π coming from?
hey what is pi,n? why do you add that, don't you just convert degrees into radians, and consider what quaudrant it's in to determine the final theta?
at 8:08 couldn't you just use only one of those answers? 5pi/6 plus pi = 11pi/6
yes
thanks i am a student from tunisia
When should we add pi and 2pi
pi when cot and tan, 2pi when cos and sin and sec and csc HAHAHAH
Thank you so much!! Now I understand the lesson a bit more. Now I know where the values came from
what about tanx=3? idk how to do it cause 3 isn’t on the unit circle
Thank you so much
Well done video
please may i ask how do you determine whether you choose the 30-60 triangle or the 45-45 triangle
Gracias ❣️
This was very well explained.
Does this include negative values of the angles?
sin(x)=-square 2/2 can the answer also be -pi/4 +2pi n?
A true hero
You are better than meenu
In the third problem why does the answers not add 2pie?
sin 3x = -cos 63
wb this one
It's Marky Mark!
How do you get the reference angle?
You're The most intelligent teacher ever ,never stop teaching i appreciate you so much i am new for your channel i think I'm doing great thanks. one thing i wanna say is believe in God and the son(Jesus ) b/c God created us for his purpose ,this world will be passed one day I'm from Ethiopia (🇪🇹) don't forget the coming of the lord
I'm still not understanding how you get 5pi over 6 inthe first problem. You would take the sine inverse of 1/2 to get the answer and it has a restricted domain of negative pi over 6 to positive pi over 6. Youre doing the same thing in another video. I just dont get how theres an inverse rule of which quadrant the answer is from and how you get 5pi over 6 that goes past the domain boundary. Please explain to me. I would really like some answers to my questions on both of your videos
I dont think the boundary applies in this situation. The boundary is more for graphing than anything else I think
Graph the equation (sinX) then type in y=K(y=1/2 in th3 first example) Then the first two times the graph crosses the line y=1/2 are the 2 (main) solutions. :)
Also: to get the second cosine, make the x negative and add 2pi, or after add 1 period to get the value of both cosines.
I don’t get why are we adding 2pi to sin. 0:54
2pi=360°=1 revolution just adding 1 revolution to find next sin that is also equal to 1/2
how do you solve it when it's in parenthesis like
tan(theta/2 + pi/3) = 1
I have a question if I am allowed to find the sin, cos, and tan in the calculator. should I still use the unit circle?
No, unit circle means nothing if you are allowed to find the sin, cos and tan in the calculator
OH RIGHT I forgot they have different periods. In class they just started giving solutions with no explanation, and I had to figure out what the hell they were doing. I figured out the unit circle bit, but didn't understand why some answers were adding different multiples of pi.
But how do you do it with cotangent and stuff
Can we get one which is more simple I’ve never heard of half of this stuff when I did it in class
How would you solve it when the equations look like this: 7 sin(3t) = -2
It's not just sin (x)
Nancy who are you
Hi, I know how to solve it now (:
Let 3t=u, solve for u, sub for 3t, write in terms of t
I understand this is 4 years late but what about non special values. For example you use 1/2 and √2/2 but what about 1/3?
1/3 is not one but root3/2 is and that one is for pi/3 and pi/6.
Bruh u literally just said do you sinX = 1/2 by JUST KNOWING that sin (Pi/6) = 1/2 HOW?????
We had to memorize it for exams, as well as the angle identity laws. Fml.
memorization makes school feel like slavery
If you memorize the 30, 60, 90 triangle, which the sides are a = 1, b = root3 and c (hypotenuse) = 2, you get sin = 1/2
Unit circle...
You don't have to memorise it. You can just use the trigonometric triangle - search it up. Very easy to draw. Just need to remember the lengths of each side (1, 2, and root 3) and you can quickly sketch it out/refer to it whenever you need to find an angle.
@0:08 what is the value of x ..... and then @0:19 you know the answer... how on earth did you solve this??? it is supposed to be algebric calculation or formula or equation... If we already know the x, why are you asking to solve it??? lets say you have sin x = 240... how do you find x?? do you use logarithm? e ?
sir how can i solve the equation of sin(x)=1/3? pls help
But what if it doesn't equal to 0? what if it equals to 1?
thanks steve
Video was helpful but still confusing
THE BESTTTTTTT
One thing, the solution just after 8 minutes- 5pi/6 and 11pi/6, each + pi. You only need 5pi/6 + pi, no?
This is a bit late (about a year, apparently) but yes, you are correct. That's because in this problem the solutions are 180 degrees apart so the periodicity is pi (or 180 degrees) and the answer is as you state above.
In 0.51 why did you add 2pi
Because Of coterminal Angles. He was trying to imply that 13 pi/6 has the same as 5 pi/6 because the problem states that we must find all the solution therefore, we must add 2pi into 5 pi/6 as they will just result into the same value
Uhm how do u know the degree that gives the quadrant e.g 150°=- 3/3?
The unit circle..? I think thats what ur referring to.
so n is just anything. WTF is n meant to be. Integer? When did graphing come into this? 1:20
n can be any integer (-2, -1, 0, 1, 2, etc).
Whenever you add 2pi *n to the original angle, you can think of this like doing one revolution around the unit circle (which is 2pi units long) and you end up in the same location, and the sin/cos or their inverse will give the same value.
ive left more confused then when i arrived i have been at it for weeks and still dont know how to write trignomic equations
I love O.C.
What if its sin 2x = 1/2?
Ə Qadanı alarame sənin. Thanks a lot!
Dude is it me or is anybody else super confused. No offense to this dude cos I've watched so many vids and am still lost. This was probably the most clear but I'm still confused.
Tanner York you have to know how to do this before the video pretty much lol
can we talk about how my boi had negative square root of 3 /divided by 3 and then just disregarded the numerator when he drew the triangle? talking bout some 1, 2, and square root of 3? Like...what? where the heck did 1 and 2 come from??
Still confused
Why is pi even in here
wdym bro
Radians😢
π is in there, because radians are used a lot in Trigonometry. I would say if you’re taking Trigonometry right now.. really study the preliminary concepts like the unit circle. When you get really good from degrees to radians… this will all make sense to you. π/6 is 30 degrees. 5π/6 is 120 degrees. π is 180 degrees, etc and so forth.
how do u know its pi * n or 2pi *n
pi*n is for tan/cot, since their value repeat every time the angle increases by pi (you can look at their graphs, notice how the shapes repeat every pi amount on the x-axis). For every other trig function, you add 2pi*n to the answer.
So to find all solutions we have to add 360n but in my book some questions have answers such as 180n can someone please explain to me why my final exam is tomorrow and im so confused on this topic :,)
You probably figure this out by now, but I will leave this here for people who need help. if you have a solution like π/4 and 5π/4, they are π distance apart from unit circle. so you can condense the answer to π/4 + πn. if you plug in 1 to n you will get 5π/4.
@@SM-qn7sr Thank you! I was taught this but it has been a couple of years since I have done trig. This cleared the example at 8:00 up. I appreciate it!
@@SM-qn7sr I dont get it , dosent make sense isnt it supposed to be coternal angle , so it should be +360?
Brother may Allah give you bad luck. It’s 1 AM, test is in T-Minus 7 hours I have been watching this video for 2 hours and haven’t understood a thing. What rhymes with booked, cooked of course I am cooked good night now. Leaving this in allahs hands and JPs bund crack.
Hundred percent brother
😭😭😭
the reference angle for root3/3 is not pi/6...wtf
Matt if tangent is positive, then yes it is but if it’s negative then you’re right
There is literally no need for all of this you don’t need to think about the angles that will give you the same answer. We have formulas for sin cos and tan that will give you immediately the two options in terms of n
😂 😂 😂 😂 Too easy. Do solve difficult questions as well
God RICHLY enhances our territory
dito ako nagpasang awa sa trigo 3.0
i’ve never been more confused
can someone be my mentor? i badly need help.
stop switching from radians to degrees, stick to one or else its very confusing
I think some people need to know both. My teacher is making us use both. I have a quiz on this tomorrow and she even said that it will be bother degrees and radians. maybe he could have done it better in the video, but it is good to know both.
2 pi is tau.