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Writing Sine and Cosine Equations from Graphs

Given a graph of a sine or cosine function (really, what's the difference if you just have the graph?), we write multiple sine and cosine functions that generate the graph. We find the sinusoidal axis (midline), amplitude, period, increment, and use the patterns to write the equations. Two full examples are covered in detail.

Пікірлер: 78

  • @MrLump
    @MrLump4 жыл бұрын

    Thank you, I have a quiz tomorrow. I can’t stay awake in class.

  • @Mr.intentional

    @Mr.intentional

    3 жыл бұрын

    😂😂😭😭💯💯💯 I felt that

  • @shelbychung4517
    @shelbychung45172 жыл бұрын

    thank you so so so much, this was incredibly helpful. i was getting overwhelmed with my assignments because i seriously couldn’t figure out cosine functions but this video helped me out so much and i got it right away after watching 💕

  • @annushkanoor4328
    @annushkanoor43285 жыл бұрын

    you've just taught me this in 7 minutes when my functions teacher couldn't teach it to me in 80

  • @xelp435

    @xelp435

    11 ай бұрын

    What are u now

  • @heatherandersen2766
    @heatherandersen27664 жыл бұрын

    This is a great explanation. Short and sweet and to the point, I will be using it with my students. Thank you so much.

  • @dayal9289
    @dayal92896 жыл бұрын

    Bro, this is amazing!!!! Had no clue how to do it, now I totally get it

  • @ErlingGrey
    @ErlingGrey2 ай бұрын

    Been trying to figure this out all day, thank you.

  • @glitched2797
    @glitched27974 жыл бұрын

    Dude thank you SO much! All I wanted was to know if I could swap cosine and sine when using this method and you said it right away 😂 🙏

  • @cassandravanmeter304
    @cassandravanmeter3044 жыл бұрын

    Thank you so so much. Teached me more in the first minute than my teacher could do in an hour lol.

  • @eshaj8697
    @eshaj86972 жыл бұрын

    bruh- you literally made me understand two fucking periods worth of math legit within the first 3 mins of the video I'm crying 🙈

  • @TheABD101
    @TheABD1015 жыл бұрын

    The video is very helpful. I am confused about how to decide whether is a sin or cos function translation. I am also confused with whether the horizontal shift is to the right or left.

  • @scottyphelps7497
    @scottyphelps74974 жыл бұрын

    this guy is the crash course for math

  • @safwankhan199
    @safwankhan1994 жыл бұрын

    How does u find the vertical displacement for cosine graphs

  • @w9ck
    @w9ck3 ай бұрын

    if this video doesnt make me into a math genius, literally nothing will you are my only hope turksvids >.

  • @alexisl9936
    @alexisl99366 жыл бұрын

    This video is great! It helped me so much. Thanks!

  • @thezyg6311
    @thezyg6311Ай бұрын

    Doesn't the period affect the phase shift?

  • @DragonRider-cx7br
    @DragonRider-cx7br3 жыл бұрын

    Wait I’m confused at 3:24 . How did you get B=pi/4?

  • @allahm-ast3mnlywlatstbdlny164

    @allahm-ast3mnlywlatstbdlny164

    2 жыл бұрын

    B*8 = 2pi 2pi/8 = pi/4

  • @thespeedyyoshi
    @thespeedyyoshi6 жыл бұрын

    WOW! This REALLY HELPED! Thank you so much!

  • @kathytran1940
    @kathytran19403 жыл бұрын

    thank you for helping me pass my quiz

  • @waezu.9227
    @waezu.92276 жыл бұрын

    Superb content

  • @stevenferreira9315
    @stevenferreira93154 жыл бұрын

    this helped me so much, thank you!!

  • @w9ck
    @w9ck3 ай бұрын

    thank you for the information turksvids i hope this serves me well for my exam tomorrow, if not then- well...idk :P

  • @turksvids

    @turksvids

    3 ай бұрын

    how'd the exam go? good luck with your continued studies!

  • @w9ck

    @w9ck

    3 ай бұрын

    @@turksvids ur videos were in fact helpful unfortunately, my teacher acc does not want her students to succeed so the questions were much harder than the ones you explained. thank you regardless >.

  • @phn1310
    @phn13105 ай бұрын

    Amazing dude

  • @TravyScatty
    @TravyScatty3 жыл бұрын

    Dude you are going to heaven

  • @7318ify
    @7318ify6 жыл бұрын

    What happens when they ask for only one equation? Which one would you use if any?

  • @turksvids

    @turksvids

    6 жыл бұрын

    All the forms for any one graph are equivalent so it kind of doesn't matter which you use. When I ask these questions in class I usually specify the starting point that I want someone to use or say that I want one positive and one negative of both sine and cosine or something like that.

  • @7318ify

    @7318ify

    6 жыл бұрын

    Ok thanks!

  • @user-yy3xd4vl8s

    @user-yy3xd4vl8s

    3 жыл бұрын

    @@turksvids what how do you get a to negative when you c sub 1 is middle and in the next examples c sub 1 is now positive even tho middle

  • @tonnymelendez7451
    @tonnymelendez74512 жыл бұрын

    I learn NOTHING from my teacher, but when I watch a KZread video, i learn?

  • @roshanshah4729
    @roshanshah47295 жыл бұрын

    how do we know when to put a negative sign in the equation?

  • @turksvids

    @turksvids

    5 жыл бұрын

    If it starts in the middle and goes to the minimum it will be negative. If it starts at a minimum it's negative.

  • @bunnydream2087
    @bunnydream20876 жыл бұрын

    for the increment, why is it found by period/4 and not period/5? i thought it would be period/5 because there are 5 main points that are used to graph one period, and 5 total increments needed to make one period--- as you stated at the end of the vid

  • @turksvids

    @turksvids

    6 жыл бұрын

    We want to break the full period into four equal pieces so we divide by 4. If you take a segment that has its two end points that gives you two points. to cut that in half takes another point, so you're up to 3 points. Now divide each of the two segments you have in half. That gives you four segments of equal length and 5 points to make it happen. So that's a kind of long winded explanation of why it takes 5 points to cut it into four equal pieces.

  • @bunnydream2087

    @bunnydream2087

    6 жыл бұрын

    turksvids thanks, that makes sense :)

  • @pandahot586
    @pandahot5865 ай бұрын

    Excellent 🎉 thanks bro

  • @turksvids

    @turksvids

    5 ай бұрын

    no problem! good luck with your studies.

  • @clumzzii
    @clumzzii3 жыл бұрын

    thanks man needed this

  • @bhavyahemnani2243
    @bhavyahemnani2243 Жыл бұрын

    Very helpful, thanks!

  • @harshdadhich9164
    @harshdadhich91644 жыл бұрын

    this man is a fucking legend

  • @ethanawakening951
    @ethanawakening9514 жыл бұрын

    i've never used pi while making the equation for graphs... Why are you using pi?

  • @turksvids

    @turksvids

    4 жыл бұрын

    Without rewatching the video I'd say I'm using pi because the period of the function is not a multiple of pi, but is instead probably just an integer. If the period is 10, for example, then B = 2pi/10 = pi/5, so you'll have to use pi when you write your equation. It's really common to have to do that since trig functions often model things that move over time and time is usually not measured in terms of pi.

  • @slkeology
    @slkeology5 жыл бұрын

    what if you are not given the sinusoidal axis?

  • @turksvids

    @turksvids

    5 жыл бұрын

    One way to find the sinusoidal axis is to average the maximums and minimums. Hope this helps!

  • @chloejacob654
    @chloejacob6544 жыл бұрын

    How to calculate the shift verticle

  • @turksvids

    @turksvids

    4 жыл бұрын

    It's the average of the maximum and minimum of the function. Hope this helps!

  • @eamonhshs2026
    @eamonhshs20267 ай бұрын

    very helpful

  • @angelantonio3147
    @angelantonio3147 Жыл бұрын

    Really good man thanks

  • @rbthesunsetloner
    @rbthesunsetloner6 жыл бұрын

    Thanks a bunch for this! Really helpful!

  • @joshsecrieru6789
    @joshsecrieru67895 жыл бұрын

    Excellent.

  • @oki_doki_do
    @oki_doki_do5 жыл бұрын

    why is the x inside the parentheses?

  • @turksvids

    @turksvids

    5 жыл бұрын

    When then x is in parentheses, B(x-C), the horizontal shift is just C units. If the x is not in parentheses, Bx-C, then the horizontal shift is C/B, which is a bit more confusing and a little more difficult to work with. If you're teacher/professor wants you to not have B(x-C) in your final answer you can always just follow what the video describes and then distribute the B at the end. So something like pi/2(x-3) would become pi/2*x - 3pi/2. hope this helps!

  • @turksvids

    @turksvids

    5 жыл бұрын

    *your

  • @zazafiend
    @zazafiend3 жыл бұрын

    Bless

  • @arielrickers4757
    @arielrickers47575 жыл бұрын

    Where did you get the 0 from

  • @turksvids

    @turksvids

    5 жыл бұрын

    I had to pick an x-coordinate for a starting point for the pattern. Looking at the graph the key points in the pattern are imiMi (intersect, minimum, intersect, Maximum, intersect). Using 0 lets you start at the beginning of the pattern. I try to explain it around [3:18] in the video.

  • @sponji4935
    @sponji49355 жыл бұрын

    How do you get phase shift?

  • @turksvids

    @turksvids

    5 жыл бұрын

    I take everything in the argument of the trig function, set it to zero, and solve. So if you have sin(3x-pi/4) + 2, I take 3x-pi/4 = 0 so x = pi/12. The curve is shifted pi/12 to the right. If you had -12cos(5x+3pi/8) + 7, I take 5x+3pi/8 = 0 so x = -3pi/40. The curve is shifted 3pi/40 to the left.

  • @aidenhall5301
    @aidenhall53015 жыл бұрын

    Thank you so much

  • @salmanzahid6910
    @salmanzahid69102 жыл бұрын

    Helpful, but still struggling to find out C

  • @turksvids

    @turksvids

    2 жыл бұрын

    Usually when I do these I pick C and then base the pattern of the graph on that. So if I pick a C value and it's at an i and goes to an M, then I'm looking at positive sine. If I pick a C and it's a minimum, then it's a negative cosine, etc. So mostly you pick C and go from there. (If you're in a class the teacher would probably pick C for you...) Hope this helps! Let me know if it doesn't.

  • @johnpringle9967
    @johnpringle99674 жыл бұрын

    Maybe It's just me, being older and such, but man! you need to slow down on your verbal speed! A lecture at warp-factor 9 is almost impossible to understand. Not only that, but some of your written notes on screen are not comprehensible! I'm sure you understand extremely well what you are doing, but the reason we viewers are watching is because we don't.

  • @turksvids

    @turksvids

    4 жыл бұрын

    Hit the gear and slow it down if it's moving too fast for you. Or perhaps just watch another, different, slower video? I find pointing out to others that they can do that is a bit easier than me changing how I talk. I change the speed on tons of videos. Never thought to tell the creator to change...

  • @johnpringle9967

    @johnpringle9967

    4 жыл бұрын

    @@turksvids My apologies Sir. It is my short-comings. It's just that you have a lot of valuable info in your videos and I like to glean as much as possible from them.

  • @jfig7682
    @jfig76828 ай бұрын

    thank u so much

  • @KhanhNguyen-gd8fv
    @KhanhNguyen-gd8fv4 жыл бұрын

    thanks

  • @TacosvsCreepers123
    @TacosvsCreepers1236 жыл бұрын

    thanks so much !

  • @Nic_Chy
    @Nic_Chy Жыл бұрын

    Ur a legend

  • @gabestoorich6377
    @gabestoorich63775 жыл бұрын

    Tanks bai, CPM is rell failure dawg.

  • @Drforeverok
    @Drforeverok8 ай бұрын

    god damn u are smart

  • @turksvids

    @turksvids

    8 ай бұрын

    I spend a lot of time thinking about this stuff and how to get people to understand it!

  • @Drforeverok

    @Drforeverok

    8 ай бұрын

    well thanks so much, I got my finals today so this came in clutch - thanks!@@turksvids

  • @chadfoy290
    @chadfoy2905 жыл бұрын

    I got lost at 5:00

  • @chadfoy290

    @chadfoy290

    5 жыл бұрын

    How did u find the period

  • @turksvids

    @turksvids

    5 жыл бұрын

    I was trying to find a "good" start and stop point for counting the periods of the function. Starting at 0, which is a lattice point where horizontal and vertical scale marks meet, I looked on period away and it wasn't a lattice point, did it again and it still wasn't, and did it a third time and it did hit a lattice point, which was at x = 10. So to get from 0 to 10 I had to go three periods, which told me that each period must take 10/3. Hope this helps!