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The following properties apply to any reciprocal function:

1. The reciprocal of zero is +∞

2. The reciprocal of +∞ is zero

3. The reciprocal of 1 is 1

4. The reciprocal of -1 is -1

5. Where the function has a maximum value, its reciprocal has a minimum value

6. If a function increases, the reciprocal decreases

7. A function and its reciprocal have the same sign

The curves of cosec x, sec x and cot x are shown below: From a right angled triangle we know that: It can also be shown that: (Try dividing the second expression by cos²θ to get the first rearrangement, and separately divide cos²θ + sin²θ = 1, by sin²θ to get the other formula.)
These are Trigonometric Identities and useful for rewriting equations so that they can be solved, integrated, simplified etc.

Trigonometric functions of angles like A + B and A − B can be expressed in terms of the trigonometric functions of A and B.

These are called compound angle identities:
sin (A + B) = sin A cos B + cos A sin B sin (A - B) = sin A cos B - cos A sin B cos (A + B) = cos A cos B - sin A sin B cos (A - B) = cos A cos B + sin A sin B
Remember: take care with the signs when using these formulae.

The compound angle formulae can also be used with two equal angles i.e. A = B.
If we replace B with A in the compound angle formulae for (A + B), we have:
sin 2A = 2(sin A cos A)
Also,
The use for this final rearrangement is when integrating cos²x or sin²x.

We use cos ² x = ½cos 2x + ½ and sin ² x = ½ - ½ cos 2x which we can integrate.
Using this double angle formula for tan 2A and the two identities:
We can replace 2A with x and use T for tan(x/2).

This gives us the following identities, which allow all the trigonometric functions of any angle to be expressed in terms of T.

The formulae we have met so far involve manipulating single expressions of sin x and cos x. If we wish to add sin or cos expressions together we need to use the factor formulae, which are derived from the compound angle rules we met earlier.
The compound angle formulae can be combined to give:

2sin A cos B = sin (A + B) + sin (A − B)

2cos A sin B = sin (A + B) - sin (A − B)

2cos A cos B = cos (A + B) + cos (A − B)

−2sin A sin B = cos (A + B) - cos (A − B)

If we simplify the right hand side of each of these equations by substituting

A + B = J and A − B = K, we create the factor formulae:

The factor formulae allow us to add and subtract expressions that are all sines or all cosines. If we wish to add a sine and a cosine expression together we have to use a different method.

This method is based upon the fact that combining a sine and a cosine will generate another cos curve with a greater amplitude and which is a number of degrees out of phase with the graph of cos θ.

This means that it can be written as R cos(θ - α), where R represents the amplitude and α represents the number of degrees the graph is out of phase (to the right).

The solution is based upon the expansion of cos(θ - α).

Write 5 sin x + 12 cos x in the form R cos (θ - α)

R cos (θ - α) = R (cos θ cos α + sin θ sin α)
By matching this expansion to the question we get:
R cos θ cos α = 12 cos θ and R sin θ sin α = 5 sin θ
This gives:
R cos α = 12 and R sin α = 5
By illustrating this with a right-angled triangle, we get,
Therefore: 5 sin θ + 12 cos θ = 13 cos(θ - 22.6)

It has a maximum value of 13 and is 22.6 o out of phase with the graph of cos θ.

Note: This procedure would work with Rsin(θ + α).

Check to see if you can get a similar answer - it should be 13 sin (θ + 67.4)

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The following properties apply to any reciprocal function: The reciprocal of zero is +∞ The reciprocal of +∞ is zero The reciprocal of 1 is 1 The reciprocal of -1 is -1 Where the function has a maximum value, its reciprocal has a minimum value If a function increases, the

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Male Edge Review and Results | My personal Experience of using the Device

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In this review:

I will explain in detail about my experience buying and using Male Edge

I'll tell you how I used it for the first time, what sensations I felt, and how I tuned into it

I will explain the instructions and my own observations

I'll show you how to better use the device to get used to it faster

You will learn about my routine

I will introduce you to the exercises for penis enlargement, Jelqing, and Kegels, which I performed for 15 minutes a day to enhance the results

I'll tell you how to wear the device outside the house

You will learn about possible side effects

You will see the chronology of my results, and you will know what you can count on

I also used a Phallosan Forte vacuum device, so I will compare Male Edge and Phallosan Forte

I will answer frequently asked questions

I'll show you how to buy a device profitably and how to get it in your country

After I read one of the forums where men discussed ways to enlarge their penis, I liked the idea of ​​stretching the penis using a device.

I never thought about surgery, but I really wanted to enlarge my penis, since I'm 35 years old, and all the girls with whom I had sexual relations told me that I didn't satisfy them or I had a small penis. It didn't excite them.

The problem turned out to be very serious. My doctor, a psychologist, told me for a long time that I should put up with my modest penis size, that I could learn to satisfy women with my 11 cm(4.4 inches) dick, that it's not important to women and just a psychological attitude, that a woman's size is not important.
Watch my video review of Male Edge Having listened to these stories, I saw in practice - size matters:

I could not get to the G-Spot.

The width of my penis did not allow normal friction inside the vagina for pleasure.

I always wanted to stick my dick in deeper, but the length did not allow it. I wanted to give her pleasure.

The woman's top pose didn't suit me, as the girls would just jump off my penis after a couple of pumps.

I was tired of covering my penis while she was looking at it.

I was jealous of men who had a large cock clearly visible in their underpants. They behaved more confidently. The girls on the beach would look at their swimming trunks. Yes, it is swimming trunks and not shorts like mine. Girls like to see a big dick through the fabric. They feel the power of such men and are ready to surrender to them.

Penis traction is an officially approved penis enlargement method. The effect of this technology was proven 20 years ago.

But the difficulty is that a device like Male Edge needs to be used for several hours a day for three to 12 months to see results. Not every man finds the motivation in himself and the desire to work on the length of his penis or knows how to organize and understand the essence of the process.

I really wanted to increase my penis size, and when I found out that it is possible to do this from a purely scientific point of view and without surgery, I was ready for anything. The main criterion: I did not want to risk the health of my penis and experience any side effects.

Click here to order Male Edge
That is why I initially considered using a vacuum extender, which I later acquired. It was Phallosan Forte, but after three months of working with it, I did not see much progress, although there was no pain.

This device is suitable for newbies. But only a rod penis extender with the help of its rigid structure is able to affect the process of penis tissue growth.

What devices did I consider for purchase?

You should consider buying only these devices since they are certified and officially sold in Europe and the USA:

Male Edge is the lightest, most constructive, compact, assembly-free, high-quality device.

Quick Extender Pro - a double strap holds the penis better; high-quality hypoallergenic materials, a lot of consumables, and it can be configured for comfort.

SizeGenetics is the same manufacturer as Male Edge. A classic extender, its prototype, Jes Extender, was the first-rod extender in the world that DanaMedic produced 20 years ago.

PeniMaster Chrome is the earlier PeniMaster extender model. Among the strap extenders, it's one of the best. A convenient clip helps to quickly pull the penis out of the structure. With its soft strap, it's a comfortable and effective device.

Phallosan Forte is a vacuum device that, using vacuum-adhesion technology, holds the penis head in the chamber on one side so that, using the strap, you can attach the extender to your body. There is a variety of ways of fastening - to the waist, knee, or shoulder. It uses a dynamic load that works well for the result. It is not suitable for all men since dynamic loading does not always cause penis tissue growth. The new version of the Plus device also includes a rod base. It managed to increase the load by three times.

PeniMaster PRO works on a similar principle with Phallosan Forte but has its own unique design.

ProExtender is an exact copy of Jes Extender but is sold under a different brand.

Why I settled on Male Edge:

This device captivated me with its design and functionality.

All boom extenders contain rods and mounts. It looks like bodybuilders hang pancakes on their barbells before squeezing the cherished weight from their chests. They are customizable, and it is necessary to adjust the length correctly. Using special screws like a jeweler, you must set the tension and follow the sensations, as inaccurate adjustments can affect the result. But with Male Edge, everything is very simple. There are only three levels of length and three levels of tension, and the device is already assembled, so you do not need to set up rods and adjust the tension. Just twist the rods, set your length, and adjust the tension the same on both sides, extending the rods until they click. That's all, and the device is ready to use. If your penis is up to 5 inches at first, you need to put the base in one direction, and if it's more than 5 inches, put it in the other. That's the whole setup.

The device is lightweight, which is especially important when you are going to use it daily for a long time. Like it or not, wearing a device with aluminum rods is a load on the penis. It all affects your comfort and ability to wear the extender for several hours a day.

The device is compact, and it can be hidden in a special small case.

The device is durable: all settings are accurately set and saved, and special comfort pads make the contact between the head of the penis and the device natural, soft, and comfortable.

I liked the price, and throughout the entire time of use, I did not have to buy spare parts.

The device is officially approved by the FDA as safe and effective. Clinical studies and customer reviews are posted on the company's website, and this immediately inspired me to buy an extender.

I do not like the idea of silicone loops that other extenders offer. I read that this is anatomically incorrect and uncomfortable. The strap mounts are much more comfortable. Any friction to the head of the penis is essential. Therefore, you need to minimize this friction with a strap, firmly holding the penis in the structure.

My first experience using Male Edge

I read in detail the instructions that came with the kit. I also watched the video instructions and reviews. Everything seemed to be ready for the first setup. I unpacked the device and was surprised that it was already assembled.

This enthralled me, as all the other rod extenders require an assembly and setup that can last a couple of hours. While wearing, set the length, unscrew the screws, and walk around to feel the sensations. How can you navigate if you are still a beginner? You do not know the required tension force, so you do not understand the correct length.

But with Male Edge, everything is much simpler. I immediately set the initial tension and fixed the base with the right side on the extender in accordance with my penis parameters.

I used the minimum length of the rods, as my penis is small. I used the comfort pad, putting it on the head of the penis, threaded my penis into the ring and secured it with a net strap.
Everything is ready and the device is already working. I feel the tension created, and it is quite comfortable.
Thirty minutes pass and it is becoming not so comfortable for me, but I know that I need a week to get used to it (the manufacturer speaks about this).

Another half hour and I remove the device, look at my penis, and do not see any redness. There is no pain after removing the device. I try to put on the device again after two hours and withstand the load for another half hour. I feel for the first time it is enough.

A week later, I began to wear the device every day, gradually increasing the wearing time. After seven days, I could stand it for two hours without taking it off. What cool progress! I tried to go out with it wearing wide trousers and ride in a car.

Everything was quite comfortable. At first, you just think that you have an extender in your underpants. And then I even forgot about it or did not focus on it. After all, I remembered why I was doing all this.

Motivation

After a week of use, I wanted to measure the penis to see the result, but it still was not enough. After all, for the growth of the penis, you need at least two months of use.

In this case, of course, there is pain, and you have to remove the device in order to go to the toilet, so you want to choose the right time to wear it while you are at home.

Imagine all the time you need to look for a moment to wear it, get it out of the box, and put it back in. It's good that I live on my own and not with a girlfriend because all of this is very inconvenient, but it all depends on your desire to increase your penis. It was just huge for me.

Every day I told myself I was moving towards my goal. And this was incredible! I no longer sat idly by. I didn't risk my health lying under a scalpel in the hospital. I did not take any pseudo pills for enlarging the penis.

I really stretched it and I was already looking forward to the moment when I would take off my underpants and the girl would see the size of my dick and start to suck it avidly, and then we'd have hot sex and she would get a vaginal orgasm because the length of my cock is finally enough to stimulate her G-Spot.

The result after one month - it was already the coveted 0.5 inches. That was all I needed at the initial stage - to believe in myself, to believe in my strength, and to trust Male Edge.

Visit Male Edge to order the penis extender

Now everything has become different: I gained experience, I trained my penis, I didn't notice it during use anymore, I increased traction in the extender and I saw that it would soon be possible to change the side of wearing the base since my member was more than 5 inches long.

Two months was easy for me to work with - I'm used to wearing the extender, I saw the result, I was reaching my goal and wanted to strengthen the effect. I began to learn Jelqing and Kegels techniques so that I'd achieve even better results.

This is what users advised on the forums. It turned out that the exercises are simple and help stretch the penis with your hands effectively. The diverse load on the penis enhanced the results. Every day I spent at least 15 minutes on this.

In the second month, I was able to increase my penis slightly - only another 0.3 inches. At the same time, I could already wear the device for up to two hours a day.

Three months became key to getting results. My dick got a whole 1.5 inches longer, and I saw the growth potential.

I kept increasing the duration of wearing the device, and for three months without a break, I wore it for 1.5 hours, then a little rest for a couple of hours, and again for 1.5 hours. At night, I put on the extender for an hour and went to bed without it.

Sometimes at night, I put on the Phallosan Forte extender, as its design allows you to do this.

In the fourth month, I began to connect with Phallosan Forte more and more actively to differentiate the load at night. My cock was already 2 inches longer and 0.5 inches wider. I saw progress, and my motivation was at the maximum.

At five months, the results stopped. A whole month and nothing. Neither the length nor the width changed. But I saw another positive point: my erection became much stronger than before. This was because I actively worked with the extender and exercises. So, the fifth month did not make progress on penis growth but helped make it stronger. This is a good result.

At six months, I was able to increase my size by another whole inch. At this point, I had seen the difference before and after. It is longer, wider, and it looks much better. I already felt more confident with girls.

The seventh month was final in using Male Edge. Another half-inch longer and half-inch wider while the erections became much stronger. I felt like a real lover and women noticed my self-confidence. Not only did it become easier to get to know them, but I also began to satisfy them more than ever.
Was it worth it? Of course! Both physiologically and psychologically, I felt like a winner.
First of all, I would like to tell you about my impressions of Male Edge. This tool for stretching the penis really won me over at first sight, especially for its ease of use, lack of need for additional parts, and the complex second configuration.

It is not like those penis enlargement extenders available online. And despite the street credibility and trust of these devices and their manufacturers by some, they still did not inspire confidence in me.

The penis stretching technique using a boom extender strap is very rigid, and it, therefore, gives a result. But it repels many men because of the use of technology for penis traction.

You need to be accustomed to Male Edge in order to use it properly and make sure that it is comfortable for you. It is important to understand that even the first week of using this device delivers certain inconveniences, discomfort, and pain - and this is a normal reaction for the first time.

This is an unusual device for penis enlargement. It does not look like any of the ones I know. On the one hand, I didn't want to put a structure on my penis that would stretch it. The penis is a very delicate part of the body, so I did not want to hurt it and then deal with the consequences.

What if I don't succeed? What if I wasted time? What if I damage my penis? What if I have side effects or never have an erection again?

These fears concern not just you but also every man before buying an extender. It is important to stay calm and remember the following:

A quality extender can never harm you when used properly.

Male Edge is recommended by the FDA. It is a trusted device that is used by hundreds of thousands of men around the world, and their reviews are available to read on online forums.

The device has a mild effect, and you are in full control of the process.

Fears and concerns develop after about a month of using the device when the first results appear. You have to understand that this will happen.

Your penis will indeed become longer and wider, your erections will become much stronger, and the duration of sexual intercourse will grow considerably. This is a direct consequence of the fact that you are doing everything right: you are using the correct settings and everything is going according to plan.

For myself, I have concluded that the use of the extender should not be chaotic. You should follow the planned strategy.

Initially, I bought Phallosan Forte and used its mobile app (now only available on Android). I don't know why other manufacturers do not do the same since it is difficult to plan your routine.

What needs to be noted constantly?

How long are you using the device on a daily basis?

When are you taking breaks?

How long before you achieve results and what sensations do you experience?

What do I mean?

First of all, you should feel the tension, you must correctly set the length of the rod, you should feel when you restrain your penis, and you should take a break, change the settings, and check the mount. Check if the penis head is firmly locked in the device. If the settings fail, there will be no result.

I've never had problems with Male Edge, because I read the instructions and looked at a couple of videos. I made up my own strategy, which I designed in Excel.

I regularly recorded my data, and it helped me to analyze everything, what was happening with me, with my potency, and with the length and width of my penis.

I recommend you repeat my experience and create your own strategy. This helps to reduce the time of using the device and increase its productivity and effectiveness.

Now let's talk about what, where, how, and how long you can use this device. The best place to use Male Edge is your own home.

If you have no roommates, you can put on and take off the device where and when it's convenient. But what if you live with your wife, children or parents? What do you do in this case?

The device is easy to put on underclothes so that it is not seen. It is also compact, so you won't have to constantly correct it while wearing it. You do not need to draw attention to the fact that it is under your pants.

This is important, and it applies exclusively to this device because other devices are bulky and inconvenient. Male Edge may scare you with its complex design structure, but it is really comfortable.

You can order Male Edge to be delivered internationally. Use code MALE10 to get 10% off.

I understand it is difficult to justify the decision to use a device to stretch your penis, because it will, to some extent, change your routine, especially when you are at home.

I, for example, used it at home while doing my favorite things: while taking a break from work or watching TV. I wanted to feel as comfortable as possible.

Psychologically, many men simply can't prepare themselves for this. Sometimes it's difficult to force yourself to take prescribed pills, but here you need to tune in, put the device on your penis, and walk with it and monitor the process.

Remember that your motivation is of the utmost importance, as you are trying to enlarge your penis, so there should be no doubt in your mind. Why be afraid of a device whose operation is confirmed by medical institutes and doctors?

If you want to make sure that it works, read the reviews from 1,000 men who have achieved success and regret only one thing: that they didn't start earlier.

Why is this information hidden? Why do people opt for surgical procedures and injections? After all, such procedures can negatively affect your health.

For me, it was the result of mass influence. I had heard that growing the penis in a natural way was impossible. However, there is plenty of evidence of the effectiveness of these products. Devices like Male Edge are used in a number of medical centers as a method of rehabilitation after penile surgery.

I will post this as well as my before and after pictures for you to see how it goes. You can find hundreds of photos of other men who have achieved the same results.

I do not regret at all that I chose this particular extender. I was dissuaded by many to engage in penis enlargement, especially without a doctor, but I decided to figure it out myself and it was very simple, as I am sure it will be for you.
My dick has become larger, and it inspires confidence in my sex life. Click here to order Male Edge

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Male Edge Personal Review After 7 Months. My Results, Tips and Tricks

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I know everything about Male Edge extender as a user, I know what information are you looking for and I will reveal the truth in this review.

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C3 and C4

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AQA C3 revision videos and exam question examples for each topic

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AQA C3 revision videos and exam question examples for each topic

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http://www.examsolutions.net/maths-revision/syllabuses/AQA/period-1/C3/module.php