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4.6 - Video 2 - Graphing the Cotangent Function - Duration: 3:52.
To determine the graph of the cotangent function, we could follow the same process that we did
for the tangent function.
However, we're going to use this opportunity to explore graphing reciprocals of functions.
Graphing reciprocals is not difficult, but it does require a little bit of thought to
understand it.
Before we can get into the graphs we just need to think about reciprocals in general.
The reciprocal of x is 1/x.
If x is very large then its reciprocal is very small, and if X is very small then its
reciprocal is very large.
Specifically, if X is greater than 1 then the reciprocal is between 0 & 1, and if x
is between 0 & 1 then its reciprocal is greater than 1.
Negative values behave similarly.
The only values that remain unchanged when you take the reciprocal are +- 1.
When it comes to graphing reciprocal functions we have another property to add that is just
an extension of this.
If f(x) has a 0 at some point then the reciprocal function has an asymptote there, and if f(x)
has an asymptote then the reciprocal has a zero.
With these ideas in mind we can now graph the reciprocal functions.
The cotangent function is the reciprocal of the tangent function, so we will start with
the tangent function.
First, we will copy the relevant information from the graph onto a number line we need
to keep track of the locations of zeros and asymptotes, as well as keep track of whether
the tangent is positive or negative on the various intervals.
We will now make space on the graph to draw the cotangent function.
We need to turn all the asymptotes of the tangent function into zeros and all the zeros
into asymptotes.
This information can then be placed on the graph.
The numbers +- 1 are fixed points under the reciprocal, so we will mark these as well.
To determine the behavior of the cotangent function near its asymptotes, we just need
to look at whether the tangent function is positive or negative there.
Since taking the reciprocal does not change the signs, this will tell us whether the function
is approaching positive or negative infinity.
Once we have all this information we can create the graph by simply connecting all these ideas
together.
This has a very similar shape to the tangent function except that it has been flipped and
shifted.
It is important that you recognize the steps involved when graphing the cotangent function
as the reciprocal of the tangent function.
Specifically, you need to understand how the roles of 0s and asymptotes switch with each
other, that signs don't change, and that +- 1 are fixed points.
The fundamental cycle for the cotangent function is (0, pi), and here is the chart of key values.
The process of graphing transformed versions of the cotangent function is similar to the
process we've already developed and practiced for the sine, cosine, and tangent functions.
Example: Graph y = -2 cot(x/4).
We first determine the fundamental period by setting the argument equal to 0 and pi.
This shows us that the fundamental period will be the interval from 0 to 4 pi.
We break this into sub intervals and get that the key values will have x coordinates 0,
pi, 2 pi, 3 pi, and 4 pi.
We can then calculate the y coordinates by substituting for the trigonometric function
and then we can put these pieces together to get the graph.
As you can see from this video and the previous one, the technique of graphing using key values
extends beyond just the sine and cosine functions.
We've now seen how to graph both the tangent and cotangent functions using the exact same
ideas.
The fundamental periods are different and the shapes of the graphs are different, but
the ideas carry forward.
In the next video, we will look at the graphs of the secant and cosecant functions.
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Rambo The Video Game - Shingo Review #025 - Duration: 10:23.
For more infomation >> Rambo The Video Game - Shingo Review #025 - Duration: 10:23. -------------------------------------------
The Pathway to Great Singing (Workshop Video 1 of 4) - Duration: 24:55.
The promise of this video is simple. I'm about to make your singing a whole lot better.
Your life a lot more fun. And your impact on the world a lot more significant.
It's possible. Maybe singing is extremely important to you like it is for my students,
Johnny Little from Mississippi, who sings at his church to connect with other people
to try and show them what his faith means to him. Or like Timotha Lanae, a singer-songwriter
in Los Angeles who couldn't live without music and singing because it's her truest
form of expression.
Thousands of my students from all over the world have the same passion for singing as
Johnny and Timotha. They have dreams for their singing that they want to come true. However,
they have challenges with their voices.
Hi, I'm Chuck Gilmore, Founder of the Power To Sing Website and YouTube Channel, where,
with over 350 videos, 45,000+ subscribers, and 12 million+ views I teach thousands of
singers world-wide.
Welcome to my brand-new video series entitled: The Pathway to Great Singing.
I've met singers from all over the world who have problems with their voices. I've
met professionals who have gigs every night who know they're straining for high notes.
They can feel it during their songs and their voices get raw by the end of the night. Often,
they're hoarse the next morning.
They come to me for help because they're worried about losing their voices and their
livelihood.
Reaching for high notes is the most common problem singers experience. They feel their
voices straining when they're singing. If they don't sing hard and loud enough, they
sound weak and breathy. Yet, if they sing too hard, their voices tighten up. Sometimes
they crack and break. Frequently their pitches are flat or sharp.
Do you ever feel frustrated or discouraged because you want to be a great singer but
just keep falling short? Do you want to be the lead singer, but your voice just isn't
working right?
Maybe you love performing in community theater, like me. You love being in great shows. And
more than anything you want to have a great audition, so you can get the lead singing
role. There's hardly anything more disappointing than not even getting a call back. (Yes, that's
happened to me). How many times have you ended up in the ensemble instead of getting the
role you wanted?
Your confidence takes a hit every time you experience a vocal problem.
If you can relate to any of these or similar problems, please keep watching because this
video is going to help you. Significantly!
In this first video I'm going to show you a POWERFUL NEW BLUEPRINT for your singing.
You're going to discover a proven way to transform what you're already doing and become a confident
singer.
This blueprint will help you develop a reliable, consistent and powerful tone so you can make
a real difference in the lives of the people you care for, like your family, your community,
your friends and fans, or even the world.
So, if you're a professional singer but you know you've been abusing your voice, or
you've gotten really good at covering your weak spots, or you've taken voice lessons
before, but they didn't seem to help, or you're coming back from a long layoff and
you want to get your voice working again, this video will help you.
The goal of this video series is simple: to equip you with a proven plan. A plan that
makes singing fun again. And, by the way, this is not just about singing professionally
(and making a living doing it) although if you follow this plan that could happen.
It's about a plan to give you the vocal freedom to confidently sing any song you want.
It's about your voice always being consistent. (Imagine what it would be like to go into
your performance knowing your voice is going to do exactly what you want).
It's about gaining the range, tone quality and power in your voice to improve your performance.
It's about the thrill of a stranger walking up to you and saying, "I love your voice".
I only need one person to say that, and my evening's a success!
Before we begin I have to warn you. Some of the things I'm going to share may seem so
simple it would be easy to dismiss what I'm going to say. That's why before we go any
further it's critical that you're aware of two important beliefs that will directly
impact you now and in the very near future.
The first belief can best be explained by the story of when I first met the Los Angeles
Vocal Coach of the Stars, Seth Riggs. In the fall of 1996 he put on a vocal workshop at
our local high school. I attended with my wife and 3 oldest daughters.
Within a few minutes several singers were asked to demonstrate how well they could sing
as a result of Seth Rigg's technique.
These singers were impressive, for sure. And Seth Riggs taught Michael Jackson, Barbra
Streisand, Madonna, Bette Midler, Natalie Cole and many other big stars. In fact, his
students had won over 100 Grammys.
To me none of that mattered. I believed the famous stars he taught and the singers at
the workshop were born that way…born with a special gift to sing.
My belief, based on experience with my voice, taught me that unlike Seth's students, I
was not born with a special gift to sing. I knew I couldn't sing like that. I knew
my range was limited. I knew where my voice cracked and strained. I knew my vocal cords
were not built like theirs. I was not genetically capable of singing like that. To me, this
was a fact.
What about you? Do you think you're genetically limited too? Do you think it's impossible
to increase your upper range? Do you believe you'll never be able to improve your tone?
I can relate because I've experienced those feelings.
But, what if it didn't have to be that way? What if instead your vocal cords could do
much more than you realized? What if all you had to do was learn a few special exercises?
The second belief can also be explained by a story. I had taken voice lessons during
high school, college and post college. Overall, these lessons did not help me increase my
range or my confidence. I'd taken lessons from university trained teachers with master's
degrees and PhD's who were great singers themselves.
I believed they knew what they were doing and that they were doing everything they could
to help me. But since I didn't improve much, that confirmed my feeling that I was genetically
limited, and no teacher or technique could help.
Maybe your previous singing lessons never made a real difference in your voice. Your
range never increased, your break is still there, your voice still jams up, you still
strain for high notes and you're still dissatisfied with your singing.
If these are your beliefs, you're feeling right now, the same way I did...skeptical.
Skeptical there's anything that will help.
A few minutes into this vocal workshop something happened with my voice that startled me.
Mr. Riggs had the whole group of us…probably a 100 or more do a vocal exercise called "bubble
lips".
You put your fingers below your cheeks along your jaw line and push up gently to lift your
cheeks upward. Then, while saying "uh" you blow air through your lips which makes
a bubbling sound.
He played a long musical scale that took me high into my voice. Higher than I'd ever
been before. But the crazy thing is my voice didn't jam up or crack. [Demo]
I felt this sound go up into my head without any trouble. It startled me. I realized I
had just vocalized higher than ever before in my life.
"What was that", I wondered? "How could I have made a sound that high without my voice
jamming up or without it cracking or breaking?
When I went to this workshop, I believed I was born with vocal cords that couldn't
sing like those people and that there was no teacher or technique that could help.
In an instant, I had an experience that completely changed those beliefs. I easily vocalized
higher than I ever had with a teacher we'd only met a few minutes earlier!
And other people around me did it too, so I knew it wasn't an accident or a fluke!
Could I have been wrong about my genetics or that no teacher or technique could ever
help me?
With one new vocal exercise, my reality shifted in a major way.
I understand your experiences with voice lessons or workshops may not have been as positive
as this one was for me. Until this time nothing really made a difference in my voice.
Maybe nothing's worked for you. You might be wondering, "can I really solve the problems
I'm facing with my voice? Can I really get better?"
I promise you tons of singers have had these same problems and questions. Singers like:
Margareta from Sweden…was unhappy with her high notes as she sang for her yoga class.
Jared from England…solo artist who had to strain to hit the high notes
David from Israel…a professional singer who was muscled up with no high notes
Calli from Australia…who was breaking and cracking as she sang higher
Paul from Los Vegas…a busy professional singer who pulled chest
Hassine from France…a PHd student and singer who strained as he sang higher
Bajit from India…who had trouble singing from low to high notes
Mary from Atlanta…who needed more power in her voice for worship service
And many, many more.
We've all heard that voice of discouragement in our head, telling us it's impossible.
And I'm here to show you it IS possible.
Today, you're going to learn something new that be a huge shift in your understanding
of singing.
In this first video, I'm going to share a blueprint that reveals the number one critical
key to significantly, massively, hugely improve your singing.
I've prepared this blueprint for you because I've seen singers of all skill levels completely
lost and unsure what to do about their voices.
If you've followed me on YouTube for a while, you already know this is very similar to my
own experiences with my voice.
After a major fail singing a solo at church, I quit singing solos for more than 20 years.
But all that's changed now. What I'm about to teach you has completely revolutionized
my singing. Now I've performed in over 37 musicals with many lead singing roles. The
success I've experience has been a constant source of joy, excitement and fulfilment.
It's possible for you to have this same success! It's made everything better with
my singing and my life, and I want you to have that too! It's the whole reason I'm
doing this.
The transformation in my voice began when I experienced that moment in the vocal workshop
when the vibration shifted into my head without any tension or breaks. I wasn't sure what
I'd felt because I'd never experienced anything like that before.
I knew I couldn't sing that high, because I'd never come close to those pitches.
However, this moment in this workshop showed me I was mistaken about my voice and maybe
this technique was different and might help me in a way I'd never experienced before.
Six weeks later I started experiencing what seemed like miracles in my voice.
I sang from the E above middle C to the F just one ½ step higher. I'd never been
able to do that, and I was 43 years old.
Now my upper range has increased by over an octave, the quality of my voice has enriched,
and my confidence has grown significantly!
I developed vibrato, something I didn't think was possible. My first teacher told
me, if you aren't born with vibrato, you don't have it. But she was wrong!
After this I started auditioning for musicals and eventually was cast in lead singing roles,
which is exactly what I'd been hoping for. Roles like Daddy Warbucks, Don Quixote, Fagan,
Peron, Captain Hook, Scrooge, The King (King and I) and many others.
My students are experiencing similar successes.
For example, Stu Thaler from Arizona. Stu always played music and sang. After his retirement
at age 62 he started a band but needed to work on this voice. He was struggling on the
high notes. Within one week of doing special exercises the high notes got a lot easier
and Stu's band got a lot better.
Katie Marshall is a 25-year-old dancer from New Mexico. She was in the cast of "A Chorus
Line" and was having a problem with a solo. It was high and she could only sing it very
lightly. Within a few weeks she was able to gain much more power. Her director was so
impressed he told her she probably didn't even need a microphone anymore. Now Katie's
a singer who can dance!
And then there's singer-songwriter Timotha Lanae who I mentioned earlier. After singing
in a concert with Stevie Wonder, she wanted to get serious about working on her voice.
Even though she's a professional singer, she knew she was cheating her way through
some problem areas of her voice. With just a few weeks of work her upper and lower range
began expanding as her middle range got more and more solid.
Everything I'm about to share with you is exactly what's helped Stu, Katie, Timotha
and 100's of singers worldwide. It's the same thing that's helped me get so many
lead singing roles.
This is what's available for you!
Now, I'm going to give you the critical key. The key to improving your singing, and
reaching the success and joy that's waiting for you!
The Bridge Blueprint.
I've mentioned something called the blueprint. The full name is The Bridge Blueprint. The
purpose of the Bridge Blueprint is to help you get on the pathway to becoming a great
singer.
To get started, I created a PDF to give you more value from this training. You'll see
the download link either in the description below if you're watching on YouTube, or
next to or below the video on Facebook or a web page. Hit pause on the video now so
you can download your own copy. Once you're ready, let's continue.
As we go through each part of the blueprint, I want you to identify any areas of opportunity
for improving your voice.
Let's get started.
The Bridge Blueprint – The Key to Great Singing
1.) What is the bridge in your voice?
It's a transition area in your voice. This is the transition you experience as you sing
from your low notes to your high notes.
In musical terms it's called the Passaggio. Sometimes it's called the "Middle" or
"Middle Voice". Some singers refer to it as "my break area".
If you're a guy whose voice has changed, your first bridge begins at the A below middle
C if you're a deep bass, or at the E above middle C if you are a typical bass, baritone
or tenor.
If you're a girl, your bridge begins at the E above middle C if you're a low contralto,
or at the A above middle C if you're a typical alto or soprano. Young men before puberty
bridge here also. For both men and women's voices, simply speaking, your first bridge
goes up about 3-4 half tones.
Now, I'll refer to singing in and through the bridge as "bridging".
2.) There are three key parts to bridging successfully; air, vocal cords, and sound
wave vibrations:
As you sing, air from the lungs moves through the vocal cords which creates sound wave vibrations.
As you sing higher, the vibrations shift from the chest and throat into your head cavities.
As this happens the vocal cords also adjust appropriately. As the pitch ascends, vibration
or resonance shifts from chest to both chest and head together.
The chest and head resonance combined is called Mix because it's a mix of chest and head
resonance. As the pitch goes higher it becomes only head vibration better known
as
head voice.
3.) What happens at the first bridge if we can't bridge successfully?
A. Outer neck muscles strain and squeeze the vocal cords and pull the larynx higher. This
causes the vocal cords to lose coordination which causes a cracking or breaking sound.
You might yell, which can injure your
vocal cords. B. The vocal cords don't adjust as needed
and flip into falsetto C. The vocal cords let too much air through
which sounds very light or breathy
4.) Why do so many singers have problems at the first bridge?
Some singers don't. They've been born with the ability to bridge without difficulty.
The rest of us struggle because we can feel the vibration moving upward and it's strange
and uncomfortable. We don't know what to do. We panic. We go into swallowing mode and
the larynx rises as the voice jams up.
5.) What happens when you bridge successfully?
A. The outer neck muscles do not engage and squeeze the vocal cords. This allows the vocal
cords to function effortlessly. The transition from low to high notes is easy. There's
no straining, reaching, or breaking into falsetto.
B. The vibration shifts easily from the chest, to the bridge, and into the head cavities
and back down. You can sing in chest, mix and head voice without any interruption in
tone quality. You sing with confidence and power.
Bridging is the key skill that causes tremendous improvement in your voice and enables you
to reach your singing and performing goals.
Hands down, bridging is "job 1" for singers. If you can't bridge, then you'll always
be limited as a singer.
Without being able to bridge, those singers who can bridge will overtake you. It'll
get harder, not easier to sing. You'll continue having vocal issues and risking your career,
you'll be overlooked for solos and lead singing roles. You'll always be plagued
with self-doubt about your voice.
Now that you have greater understanding about the bridge, the BIG question is, how DO you
bridge successfully? That's exactly what I'll show you in the next video.
Inside this next video you'll discover your vocal type. Knowing your vocal type enables
you to choose tailored exercises specific for your voice. That means you'll learn
to bridge rapidly so you can get better faster.
It doesn't matter if you're a newer singer or a busy, gigging performer, what you've
learned here today is a game changer in becoming a great singer. It makes your life so much
more fun, and your impact on the world a lot more significant.
Before we go today, I'd love to hear from you. Tell me, what would your life look like
if you could be the singer you've always dreamed of?
How will life be different when you can complete every performance easily without your voice
feeling strained? How will it feel when you consistently get the leading roles and the
solos? How will it feel when someone says to you: "I love your voice"!
(From personal experience, it's about the greatest thing in the world)
Let me know in the comments below! I'm going to read every one, and I'll respond to as
many as I can.
If you've found this video useful, please share it on Facebook, Twitter or send the
page URL to a friend.
Bridging gives you the ability to have absolute control and freedom with your voice.
Amazing things start happening with your voice. The connection with your audience gets stronger.
It becomes easier to inspire and motivate your audience.
More importantly, what you're learning in this workshop puts you on the right path to
get there!
Next up in video #2, you'll take a vocal test to discover your vocal type!
I can't wait to see you in the next video!
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Video: Strong storms expected for Friday (7/26/18) - Duration: 3:11.
For more infomation >> Video: Strong storms expected for Friday (7/26/18) - Duration: 3:11. -------------------------------------------
Protests over kicking video continue - Duration: 0:49.
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Video shows officers saving child from hot car after grandmother accidentally locked keys inside - Duration: 0:39.
For more infomation >> Video shows officers saving child from hot car after grandmother accidentally locked keys inside - Duration: 0:39. -------------------------------------------
Paradiddle - Tap dance Tutorial - 28th video - 5 minutes - Duration: 5:21.
Hi I'm Marta, I'm here with another technical video.
I'd like to show you the Paradiddle, which is a combination of 4 sounds,
and sometimes to simplify it, I refer to it as quadriola.
First I'll show you the technique
and then I have a mini-routine to help you practice this combination.
Lift your leg up
Dig = hit the back edge of the right heel
Brush back right
Step right
Heel right
Paradiddle = dig + brush back + step + heel
Paradiddle basic exercise
Paradiddle mini-routine
Part 1
repeat
Part 2 other side
repeat
Part 3
repeat
Part 4
repeat
From the beginning
Try it faster with music
You can take those 5 minute breaks every day
Have a great week and see you next time.
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