Graphing Sine and Cosine Functions
Вставка
- Опубліковано 5 жов 2013
- Video describing step by step process of graphing sine and cosine functions. Covers: period, increment, start (which is what I call a phase shift), amplitude, sinusoidal axis, maximum, and minimum. Also explains the patterns: iMimi, imiMi, MimiM, and miMim
1:57 Is where I explain how to get all the necessary information to create a graph
4:09 Is an example of graphing a sine function
7:08 is an example of graphing a cosine function
![Graphing the Sine & Cosine Functions - [2-21-8]](http://i.ytimg.com/vi/UAHbyfvHxVY/mqdefault.jpg)
Thank you for being better than my math teacher, you deserve a raise!
you are literally a god thank you
Thanks a ton for the clear explanation!
THIS WAS GREAT THANK YOU
Hey there. Great video. Do u have a suggestion for when your start is -4 but your increment is pie/10. I'm seeing this as a pain in the .....question is y=5sin(5x+20)-2. Thanks
If I had written that question I would say that I forgot to put the pi in 20pi...as it is though you just get really gross values along the x-axis: -4, -4+pi/10, -4+2pi/10, etc. There's no good way to clean those up, so I'd just leave them as is.
THIS WAS FUCKING AWESOME
What would the equation for sin x look like if the function never drops below the x axis?
If the equation is something like y = d + a*sin(x) and both d>0 and d>|a|, the absolute value of a, then the graph will never dip below the x-axis. For example, something like y = 12 + 2sin(x).
once you find your start value, how do you find the rest of the values for your graph?
Find the increment (period/4), note the pattern, keep adding the increment and following the pattern. I definitely recommend watching through the video one or two more times. It might help.
What do I do when the phase shift is a normal integer like four but my increment is in radiants (has a pi in it)?
That almost invariably means there was a mistake in the problem that was written or in the way you found the phase shift (start) or period (increment). If that does happen, though, say the start is x = 3 and the increment is pi/5, then you just label the axis really weirdly with 3 + pi/5, 3 + 2pi/5, etc. But definitely check the problem and your values again before graphing. (If you comment the function back I'll take a look!)
if the inside is like this (-bx-c) does that affect the pattern ?
thank you so much for this video, it cleared up alot of confusion !!
for the (-bx-c) issue you use even/odd functions:
Sine is odd, so sin(-t) = -sin(t)... so sin(-bx-c) = sin(-(bx+c)) = -sin(bx+c) and then you go from there.
Cosine is even so cos(-t) = cos(t)...so cos(-bx-c) = cos(-(bx+c)) = cos(bx+c) and then you go from there.
Hope this was helpful!
turksvids so helpful !!! Have you made any videos on how to graph tangent, cosecant, and secant graphs ?
here's my graphing trig playlist: ua-cam.com/play/PL08AC52BF1DE8873E.html
@@turksvids tanks !! do you have any videos on damped trig functions ? it's in my textbook but the way they explain it is all wonky haha
unfortunately that's a topic i haven't gotten around to yet! sorry!
why did you start at the maximum? didn't we have to start with minimum first since the pattern is i-m-i-M-i?
I'm guessing you mean the second graph? That was a cosine function, not a sine function. Cosine functions start at a maximum if they're positive or a minimum if they're negative. Hope this helps!
YAS
Is it not if our sine is negative, we start below the graph?
Since graphs always start at an intersection with their sinusoidal axis (S.A.). If the function is negative then you head toward a minimum; if the function is positive you head toward a maximum. Hope this helps!
Hi, how would yo equally divide your intervals when if it's an ugly start?
Hi! The start doesn't really impact dividing up the intervals. The intervals are all about the period (2pi/B) and then dividing the period by 4 to get the increment (P/4). Once you have that you write the start and the increment with the same denominator, start at the start, and then just keep adding the increment.
@@turksvids thanks but the distance from center to the first point(bx -+ c = 0) is not the same as the distance from first point to second point (P/4) so wouldn't my scale be uneven?
@@turksvids and also why would you need to write them as the same denominator
Are you talking about the distance from the first point to the y-axis? I often put the y-axis in at the end since it doesn't really help with anything but the vertical scale. The distance between all of the key points of the graph (iMimi or MimiM, for example) is always the same.
You don't need to, but if you're going to add or subtract fractions then at some point you'll want a common denominator.