How do you determine the phase shifts for sine and cosine graphs
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- Опубликовано: 15 окт 2024
- 👉 Learn the basics to graphing sine and cosine functions. The sine graph is a sinusiodal graph with x-intercepts at x = 2n*pi, maximun value of 1 at x = pi/2 + 2n*pi and minimum value of -1 at x = -pi/2 + 2n*pi. The cosine graph is a sinusiodal graph with x-intercepts at x = n*pi/2, maximum value of 1 at x = 2n*pi and minimum value of -1 at x = (2n - 1)pi. To graph the sine and the cosine graph, we plot the above points on the x-y coordinate plane and graph accordingly.
After we have graphed the parent graph, we then apply the required transformations to the sine/cosine graph. The amplitude is the maximum point on the graph, the period is the distance/time for a complete oscillation, the phase shift is the horizontal shift from the parent function, the vertical shift is the vertical shift from the parent function.
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![Phase Shift of Sine & Cosine Graphs (Sinusoidal Waves) - [2-21-13]](http://i.ytimg.com/vi/1zButVPQsLo/mqdefault.jpg)
![Phase Shift of Sine & Cosine Graphs (Sinusoidal Waves) - [2-21-13]](/img/tr.png)
This dude deserves every single one of his subs and more. When khan academy is not really helpful, I look to here and to OCT and I honestly think you both deserve more subs as well as a pay raise.
Finally! An explanation as to why the phase shift of the cosine graph is so damn tricky! Thanks a million.
Lenny Shelby you are very welcome!
Whenever I search up a math question and I see a Brian Mclogan video, it's always a no-brainer to watch because it's always time well spent! Thanks, Brian!
This video probably saved at least 40-60% of a test. Much love
you are very welcome! best of luck!
Dude man, I spent an hour trying to understand "mylabs" technique and still couldn't get it, and here you are teaching me the concept in 7 minutes. You are such an amazing teacher
I think this is the best video about this on RUclips. Literally a life saver
happy to be able to help
better than khanacademy
thanks!
Thanks. This the only video that made it clear for about the phase shifts!
+Majd Semaan awesome! they get a lot of people, happy to clear the confusion for you
Thank you for making these videos. Helped me understanding my online Trig class much better.
you are very welcome! happy to be able to help you out!
Aha! Setting the transformation equal to zero makes so much more sense to me now. Thank you sir!
I'm teaching my Pre-Calc classmates your "initial period" trick as the "McLogan Method" lol. Before that, everyone was wracking their brains so much on calculating the x-axis values when there's a phase shift.
Just wanna say. Thank you for your help. I’ve never been the greatest at math but your videos truly help!!!!!!!!
This video needs over a million views.
Couldn't even learn this in class and I learned it on RUclips! Thank you!
Now you know!
For me I learned that you can factor what’s in the function in order to get the phase shift. It was always confusing why you would do it and also trickier in some instances. Now it makes a lot more sense with it equaling to zero. Great vid.
Thank you so much. I really appreciate your dedication and passion for teaching. Wouldn't have been able to finish my math HW without this video haha
Always with the great videos👏
in precalculus right now stuck on this correlation yoo🔥🔥
Thanks the period kept making me get them wrong because i did not realize it impacted my phase shift also my professor gets them by doing a 3 inequality interval like 0 is less than and greater to pie(x-pie) is less than greater to 2pie but it is a longer process and throws me of but thank you a million
I had a problem on my homework that read " y = 6 cos (3 x - 2) " , it was marking me wrong for answering -2 or 2 for phase shift and looking for the answer "2/3" as the face shift. After doing what you mentioned to do, in my case set 3x-2=0 I would get the answer x=2/3 or in other words c/b. I was confused with with the formula c/b because I would want to carry over the negative sign from (-2) and use -2/3. However, setting 3x-2=0 makes me realize why the answer is 2/3. Thanks for sharing the initial period information, it does help!
yeah! awesome! happy it worked for you
Thank you so much for doing these videos! If every math teacher I ever had gave a shit like you, Math would not be a struggle for me. You engage, make is simple to understand and explain these problems thoroughly. You have seriously helped me in College Trig. THANK YOU!!!!!
Sometimes your videos are better then Khan academy and thegreatcoursesplus,
cheers Amy! so happy to be there for you!!
that sigh at the end xd
Eric Raywood : )
Thank you Brian! Very helpful
Bring some glucose for the saviour !
LOL
You're a good teacher :) keep it up
Harry McDonald thank you will do
Man, I should have watched this last night, I got this one wrong on my exam. Great video, I'm a pro at phase shifting now.
haha, as you should be, now you know
I like your style and presentation Brian. You have that "math guy" look. :-) I was a high school math flunkie lol, and it took me military service and college before it all "clicked", and I'm still no guru. I remember all the people that "got it" (math that is) around me in high school and I also remember being lazy and immature. I wish I'd had more motivation but better late than never!
But what is the phase shift's role in a circle? Like if you are given a problem for a certain real-life circle and you need to write its sine or cosine function it's simple to find the amplitude and period etc. but since it's not actually on a graph, as it is a real object, how do you know its not phase displacement?
totally helped right before my test tomorrow!!!!
+David Martin happy to help, good luck
randy ortan ... Thanks
dang, your better then my trig teacher. imma senior in highschool trying to pass trig.
Don't forgot to do your English homework too.
I didnt pay attention in highschool math and am now paying the price in college thank you for these videos they help me alot
your videos are literally saving my life rn
Awesome dude, great breakdown of the calculations, I finally understood it
Need help finding out wavelength, phase shift and phase angle of an AC voltage is expressed as 240 cos(2765t - 45°).
is the phase angle -45 degrees
and is the phase shift +45 degrees?
please help thank you
Angelo Taracena not set 2765t-45 = 0 then solve for t, that will be your phase shift. If there was not a coefficient of 2765 then your answer would be correct. When it is there, it effects the phase shift so the best way to determine the effect is to set equal to zero and solve.
does the frequency affect the phase shift? for example this question for my math is y = -5 + 3cos 3(theta + pi/4) would the phase shift be pi/4 or 3pi/4? thanks
It takes a piss @ 4:50
hahaha I can't talk
these random math channels are way better than the actual teachers lmao. Then again my math teacher is good it's just that he doesn't make it fun so we don't pay attention
I just factor the pi out so cos(pi(x+1)) meaning the graph moves 1 unit to the left and since the or the inflection point is x=-1
left
hi sir! I just have a question. What is the unit for phase shift? Is it only by radians or it can be by real numbers?
would it be possible to simply factor the pi inside the parentheses and see that it's pi(x+1) and shift the equation 1 to the left
I am gonna fire my teacher and Hire you.
+ricky vij haha, here all day long for you, happy to help
you may graph any function by yourself with phase shift and intercept. And compare how the plot of the functions work on graph. Definitely the same result. you do not even a mapping such as sine function. you only need a set X and the range of the set f(X). It is tricky and it is fun.
How would you graph f(x)=cos x-3? Is the period 2pi with a phase shift of 3 to the right? How would I find the units on my graph so I could plot some points?
I'm so lost...
earlybirdhitstree yes you are correct with the phase shift and period. I would take the parent graph cos(x) and move the max/min and intercepts three units to the right. For instance a maximum point on cos(x) occurs at when x=o and 2pi. The max points would not occur at 3 and 2pi+3. You may want to use your calculator and covert the numbers to decimal form to aide in graphing
Mr. McLogan's Math Channel Oh okay!! Thank you so much!!! :-)
this was a great vid! so thankful!
you are very welcome Yannick
Good explanation, thank you !
you are very welcome! happy to be able to help!
So if you set "bx - c" equal to 0, then solve for x, that will tell you the phase shift? If so, how do you know whether the graph is shifted to the left or right based on the x value.
+John Stuart yes, x-(h) where the value of h is your horizontal transformation h positive right, h negative (h-(-h)) or (x+h) left
Very helpful video but i tried the same START/END method and what was supposedly my END POINT, actually wasn't after i added the T/4 to my starting point and to my 2nd/3rd point.
not sure where or what went wrong
Very Gd, KIUp
came here to double check my understanding but solving for x through bx-c=0 seems like a lot more work than just taking b out in front of the bracket
Thank Mr proffessor.
you are very welcome!
Very good.
Thank you so much... This helps alot
you are very welcome
So I'm pretty sure I understand how phase shift works. Or atleast I thought I did. Here is the problem.
y = -3sin(6x+π/2)
|Amplitude| = 3
Period = π/3
Phase Shift = -π/12
All of that is correct so far, but when I graphed the function it said -π/12 for the phase shift was wrong and it would only accept the answer when I made it positive. How can I be right for the phase shift, but wrong when graphing the function?
You know son, I remember when I was young like you. We played pong and not beer pong. Nintendo had this really cool game that was invented 10 years earlier. Yep, scientists had fun playing pong in the 1960's. As it turns out, that was way cooler than going to the Moon. As far as the Moon goes, Galileo realized that the Earth orbited the Sun because Venus had phase shifts like the Moon. ergo, phase shifts are cool. And I understand that this might be before your time. :) p.s., am having some fun and letting kids know that phase shifts actually have a place in the history of science.
that s really helpful thanks
you are very welcome!
so for y= -1/4cos1/3(x-50 degrees)-9 would the phase shift be +50 degrees since there is nothing in front of the x. And all together would the transformations be vertical compression by a factor of 1/4 of the original height y=cosx, phase shift = 50 degrees, horizontal stretch by a factor of 1/3, vertical translation 9 units down and reflection on the x-axis???? PLEASE HELP thank you
Sayrah Qaiser The (1/3) should be in front of the x changing the phase shift to 150 degrees. I have never seen a problem how you have it written so I would assume the 1/3 is in front of the x. If so everything else you have described is correct
Mr. McLogan's Math Channel THANK YOU so much, and does amplitude = radius
If i only have the graph, say the equation hasnt been given, but its y=sin(9.7x+4.8) - 14.8
Is there a way to find phase shift? I tried graphing heavy decimal graphs, but i find it hard to get phase shift,unless i cheat with the equation. I want to be able to do it raw, just straight numbers.
you know the parent graph of sine crosses at the origin, so you can measure how far the next intercept is for the graph and determine that to be the phase shift. You can do the same with cosine but use (0,1) as the initial point of the parent graph as the max
wish you can be my teacher, so much better at explaining than mine
GrandNecro thank you happy to be able to help you out!
Can you explain how am I supposed to know by looking at the graph if it is Sin or cosine ?
without any transformations sine crosses the origin and cosine does not, that is one easy distinction
Thank you very much
you are very welcome!
So if im given a graph, the phase shift would be the period?
+Maria fernanda Castillo no the period is the length it takes for the graph to repeat itself, phase shift is the horizontal transformation
How do we determine the (bx-c) when we are only given a graph? I understand that you can use the period to find B, but I still don't get how you can set (bx-c) = 0 when you don't have c.
+Savas_7 c is the horizontal transformations, so if there is none then it would be bx=0
I am solving a sinusoid at the moment and am wondering what the letter "b" stands for in the equation?
+Alakasam RUclips it affects the period of the sinusoid, try graphing with different b's to see the effect
It doesn't stand for anything. It's just a letter...The equation is y=asin(bx-c) + d
if you notice, they're just selecting letters from a->z to use as a variable.
How does phase shift affect the period of a graph
good explanation
thank you!
sir can u make lecture for general competition exam...
I do not know what is on a general competition exam but either way I am sorry I only have time to work on my current classes I am teaching
If you're like me and don't need the review, he gets to the phase shift at 6:40 or so
I felt that sigh at the end lol
the sigh at the end is great. lol
: )
Okay but how do you define C and B if we dont know them in a task
THANK YOUUUUUU
1:27 he meant 1 unit to the left
thanks a lot keep goin
Wrong wrong wrong.
The correct way to write the sine function is
y=AsinB(x-C)+D
The way you wrote it is
y=Asin(Bx+C)+D which is wrong. You distributed B across x, but not across C. Rookie mistake.
You shouldn't distribute anything.
If the phase shift is +/- pi then you write it as +/- pi, no matter the value of B.
Yes, I prefer that form as well. You can still determine the correct phase short by factoring out b which I believe I was trying to achieve as most equations do not have b already factored out
mr mclogan. youre mcbest
happy to help!
i wish he was my math teacher.
RESPECT
@Free Math Videos hahaha that exhale at the end tho, jokes aside thank you for the clarification
you are very welcome!
Thanks
you are very welcome!
I still don't understand how you would do this in a Real Life Situation. So lets say a ferris wheel problem came up, and you are asked to find the values of a, b, c, and d... how would we find the value of c?
This is if we are not given a graph.
+Nahian Fariha then you will want to create a graph to represent the situation
here in 2020 trying to learn math because online learning is vv difficult :O
🙋👍👍
Usually everything I hear you say makes sense but this one I am completellyyyyyy lost
PERIODTTTT
Aren't it supposed to shift to left on 1:26 min?
I did?
You said shift to the right, then drew it on the left.
i love u
happy to be able to help
Yasss
😀
4:06 he speaks Spanish
Randy ortan. 😂
Do more graphing and less talking!!!
haha, noted
I can’t watch this guy he talks to much
Would you prefer I just do the work and not talk, or are you specifically talking about this video I talk and don't do the work because I have a lot of videos
2pie/pie is pie not 2
correct
No that's wrong
2pie divided by pie is most certainly 2. The pies cancel out.
To be honest this guy didn’t explain anything