Writing Sine and Cosine Equations from Graphs
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- Опубликовано: 28 фев 2014
- 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.
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Thank you, I have a quiz tomorrow. I can’t stay awake in class.
😂😂😭😭💯💯💯
I felt that
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 💕
you've just taught me this in 7 minutes when my functions teacher couldn't teach it to me in 80
What are u now
This is a great explanation. Short and sweet and to the point, I will be using it with my students. Thank you so much.
Bro, this is amazing!!!! Had no clue how to do it, now I totally get it
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 😂 🙏
Been trying to figure this out all day, thank you.
Thank you so so much. Teached me more in the first minute than my teacher could do in an hour lol.
bruh- you literally made me understand two fucking periods worth of math legit within the first 3 mins of the video I'm crying 🙈
How does u find the vertical displacement for cosine graphs
WOW! This REALLY HELPED! Thank you so much!
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.
this helped me so much, thank you!!
Thanks a bunch for this! Really helpful!
thank you for helping me pass my quiz
This video is great! It helped me so much. Thanks!
Doesn't the period affect the phase shift?
Superb content
Very helpful, thanks!
thanks man needed this
this guy is the crash course for math
Really good man thanks
Amazing dude
if this video doesnt make me into a math genius, literally nothing will you are my only hope turksvids >.
Dude you are going to heaven
What happens when they ask for only one equation? Which one would you use if any?
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.
Ok thanks!
@@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
Excellent.
How do you get phase shift?
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.
thanks so much !
Thank you so much
Where did you get the 0 from
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.
How to calculate the shift verticle
It's the average of the maximum and minimum of the function. Hope this helps!
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
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.
turksvids thanks, that makes sense :)
what if you are not given the sinusoidal axis?
One way to find the sinusoidal axis is to average the maximums and minimums.
Hope this helps!
Excellent 🎉 thanks bro
no problem! good luck with your studies.
this man is a fucking legend
thank you for the information turksvids i hope this serves me well for my exam tomorrow, if not then- well...idk :P
how'd the exam go? good luck with your continued studies!
@@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 >.
very helpful
Wait I’m confused at 3:24 . How did you get B=pi/4?
B*8 = 2pi
2pi/8 = pi/4
how do we know when to put a negative sign in the equation?
If it starts in the middle and goes to the minimum it will be negative. If it starts at a minimum it's negative.
why is the x inside the parentheses?
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!
*your
thank u so much
I learn NOTHING from my teacher, but when I watch a RUclips video, i learn?
thanks
Ur a legend
i've never used pi while making the equation for graphs... Why are you using pi?
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.
Bless
Helpful, but still struggling to find out C
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.
Tanks bai, CPM is rell failure dawg.
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.
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...
@@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.
god damn u are smart
I spend a lot of time thinking about this stuff and how to get people to understand it!
well thanks so much, I got my finals today so this came in clutch - thanks!@@turksvids
I got lost at 5:00
How did u find the period
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!