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Revision Notes for Ch 8 Introduction to Trigonometry Class 10th Mathematics. Trigonometry and Trigonometric Ratios. > Trigonometry is the branch of mathematics which deals with measurements of angles and the problems related to relationship between sides and angles. Trigonometric Ratios: > It is the ratios of two sides of a right angle triangle. > Suppose we have a right angled triangle ABC. > Thus the trigonometric Ratios are defined as the largest side of a right angle triangle is known as hypotenuse. Also, by Pythagoras theorem, we know that h2 =b2+p2. Here, ? is pronounced as theta, ?A=?. Class: Maths (English and Hindi Medium).� Visit to Class 10 Maths Chapter 8 main page for other exercises whether download or online study. Class 10 Maths Exercise Solutions. 10th Ch 10 Maths Class 10 Icse Video Maths Exercise Solutions in English. 10th Maths Exercise Solutions in Hindi. Download 10th Maths Exercise in PDF. Class 10 Maths Chapter 8 Solution Main Page. Class 10 Maths Chapter 8 Exercise Solution in Hindi Medium Video. Class 10 Maths Chapter 8 Exercise Solution in Videos. Class 10 Maths Exercise Explanation. Class 10 Maths Chapter 8 Exercise Solution. Important Questions for Proof. 1. If A, B, C are the angles of triangl. Class 10 Maths - Basic vs Standard. Sample Papers Class 10 Solution. Sample Papers Class 12 Solution. CBSE Datesheet Boards. CBSE Previous Year Papers.� Get NCERT Solutions with videos of all questions and examples of Chapter 8 Class 10 Trigonometry. Videos of all questions are made with step-by-step explanations. Check it out now. Trigonometry means studying relationship between measures of triangle. Usually, we talk about right triangles when we study trigonometry, In this chapter, we will study.

Email: r. Please note: the suggestions below are just ideas for student experiments; they have been trialled but do not guarantee success. It is up to the teacher and student to see if they are practical for their school situation. The quality of Queensland wines is now recognised as amongst the best in Australia. Overseas exports are increasing, particularly to international markets seeking premium quality boutique wines. The Queensland wine industry has grown significantly over the years to cover a total of hectares.

The majority of this growth has occurred during the past 20 years with significant plantings throughout the southeast corner of the State. However, winemaking is still somewhat of an art but is strongly informed by science. Thus an interesting student experiment can be undertaken in this context. After crushing the grapes the next step in the making of wine is the fermentation of the grape juice and pulp with various yeasts and bacteria. Most books say that the amount of ethanol produced is dependent on the sugar concentration of the starting juice but then give four different equations depending on assumptions made such as the ratio and purity of glucose and fructose; or whether the fermentation gets 'stuck' at the primary stage.

Fermentation is an exothermic reaction so heat is generated during the process. To control the heat, the winemaker must choose a suitable vessel size or else use a cooling device.

In the case of a student experiment , you might control the temperature by use of a water bath or a refrigerator.

Fermentation at higher temperatures may have adverse effect on the wine in stunning the yeast to inactivity and even "boiling off" some of the flavors of the wines.

How temperature and the final concentration of alcohol are related would make an ideal student experiment. This is not such an important one and the effects may be small - but nevertheless important. You could repeat it with acidity as the independent variable and controlling the amount of sugar, yeast, temperature and so on. As the alcohol concentration rises the yeast cell membranes become susceptible to rupture by the ethanol.

Some yeasts are more susceptible than others. Or you could look at the susceptibility of yeasts to [SO 2 ] - winemakers use SO 2 in the form of sodium metabisulfite to kill off wild yeasts as these are less tolerant than wine yeast to the SO 2.

Sulfur dioxide is widely used in winemaking because of its antioxidant and antibacterial properties. You could hypothesise and test how SO 2 affects the performance of yeast. Two common methods for determining SO 2 in wine are included in the "sulfite" section later. Any fruit or juice works just fine although some require more sugar to be added.

Also, my winemaking unit for chemistry teachers is available online. It is worth stressing here that you should not taste the wine being produced; this is not because of the alcohol but rather because of the unsanitary conditions under which your wine is being made in a lab, not the Home Economics kitchen. If you intend tasting your wine then your risk assessment should state and evaluate that.

If I was your teacher I'd say "no" as it would not be worth the headache. The most common method is by redox titration. In this analysis, you add an excess of standardized acidified potassium dichromate solution to the wine which converts the ethanol to ethanoic acetic acid. The amount of unreacted dichromate is then determined by adding an excess of potassium iodide solution which is also oxidised by the potassium dichromate to form iodine.

The iodine is then back-titrated with a standard solution of sodium thiosulfate and a starch indicator. The titration results are used to calculate the ethanol content of the original solution. It is complex but works well and is very impressive. You have a problem if you are dealing with red wine as the red pigments mask the colour changes. In that case you have to extract the ethanol from the wine in effect, by various forms of distillation and carry on, as above, from there.

Canterbury University NZ has quite a simple method for red wine: see Canterbury - alcohol titration. Chemistry teacher Emma Hodginkson from Mountain Creek State High has performed the Canterbury ethanol titration with her Year 12s for Ch 5.3 Maths Class 10 Msds a few years and has found it very successful.

As it is a redox titration she says it works better in Year 12 when the students have completed some redox theory whereas Year 11s find the calculations a bit heavy going. To overcome the practical difficulty in locating a small container to suspend above the dichromate - they use a plastic water bottle lid suspended with cotton thread.

At All Hallows' School, Brisbane, chemistry teacher Matthew Stuart uses a more compact method: a boiling tube is used to hold the 20mL wine sample, and 8mL dichromate solution is placed in a small "fusion tube" a small diameter test tube carefully slipped into the wine sample. Some parafilm is used to seal the boiling tube, or a suitably sized stopper if possible. A pair of forceps is used to remove the dichromate tube without spilling into the wine sample, the outside rinsed with water, and then titrated.

One caution in all of this: merely measuring the concentration of the various components of a selection of wines ethanol, pH, acidity and so on may not make a good EEI. Manipulation of variables gives students a better chance of demonstrating all aspects of the assessment criteria. Alcohol content by distillation 2. Alcohol content by Ebulliometry 3. Alcohol content by boiling 4. Alcohol concentration by dichromate oxidation and titration 5. Alcohol concentration by Vinometer 6. Alcohol concentration Western Australia - Chemistry in Context.

You may have seen different types of yeast for different purposes; for example, there are beer yeasts top-cropping ale strains and bottom-cropping lager strains ; baker's yeast for bread-making; red and white wine yeasts; and even genetically engineered yeasts used for industrial alcohol production. Many are just different strains of the same yeast but grow differently.

A good research question might be: how do different yeasts affect the production of alcohol from grape juice? There is a problem however. The majority of senior chemistry investigations use 'continuous' variables; that is, any value is possible within the limits the variable ranges.

For example, temperature, pH, sugar concentration, amount mass of yeast, surface area and so on. But when you are comparing two different categories of a variable, such as type of yeast wine yeast vs.

The choice of the categorical variables is not as common as using a continuous variable in Senior Chemistry experiments, partly because categorical variables have their peculiar difficulties and this makes the design of this EEI far more complex than it looks at first glance.

It is not just a matter of comparing equal amounts of the two yeast products on the amount of alcohol produced. Do the yeasts each have an optimum pH and if so what pH will be chosen for the grape juice and why? Is surface area a concern maybe if one is a bottom fermenter, and another a top fermenting yeast.

Will a low sugar or high sugar juice be used - important as it may be the alcohol itself that inhibits the yeast. And what about the dependent variable alcohol concentration : will the rate of alcohol production be measured, or just the amount of alcohol present when the yeasts die or the sugar runs out; or will the alcohol be measured after a set time, eg 7 days?

Is time important? Some yeasts are slow eg the CY Slow White yeast from France takes its time but gets there in the end; it would be a brave decision to cut it off after 7 days. Lastly, some yeasts convert malic acid to alcohol as well as converting the sugar. Imagine using a yeast such as the Lalvin C from France which partially degrades malic acid.

Of course you'd get more alcohol out of this one. Another terrific idea for a wine student experiment. The two common fruit sugars used in winemaking are glucose and fructose. Grape juice is made up of these in roughly equal quantities. Another sugar used in the fermentation industry is sucrose cane sugar. Sucrose is frequently used as a cheap carbohydrate by breweries, wineries and other fermentation-based industries employing yeast.

It is a di-saccharide composed of D-glucose and D-fructose linked by an alpha-1,4 glycoside bond. In the initial stages of fermentation, sucrose is rapidly hydrolyzed into glucose and fructose by the action of the enzyme invertase on this bond.

Then the sugars are transported across the cell membrane where they ferment and form alcohol. So investigating the fermentation of sucrose is really also about studying the fermentation of a mixture of glucose and fructose. This suggests a terrific student experiment: to look at the reaction rates of glucose, fructose and sucrose. At the start of fermentation, grape juice contains approximately equal amounts of glucose and fructose called 'hexose' sugars. While both are fermented by wine yeasts to ethanol and carbon dioxide, Saccharomyces cerevisiae consumes glucose faster than fructose because this yeast is know to prefer glucose and so is called a glucophilic or 'glucose-loving' yeast.

As fermentation proceeds the ratio of fructose to glucose increases. Therefore, fermented grape juice will contain more fructose than glucose as residual sugar.

Fructose is the sweetest hexose sugar, approximately twice as sweet as glucose, and thus the wine gets an undesirable fructose sweetness, unbalanced by the sweetness of glucose.

So here is the starting point if you are doing a student experiment. Pose the Research Question: "How do the fermentation rates of glucose, fructose and sucrose compare? One delicious complication though is that when glucose and fructose are mixed as in the case of fermenting sucrose; or in an artificial mixture the glucose ferments faster than fructose.

Glucose seems to inhibit fructose. Hmm - now that is tricky. Your investigation could look at the fermentation rates of glucose and fructose separately - keeping everything the same except the independent variable of initial concentration. An then look at a mixture - or just look at sucrose as a natural mixture. What are you going to measure?

The progress of the fermentation can be assessed by measuring the concentration of residual sugar or of the ethanol, or by the amount of CO 2 produced. Sugar concentration can be measured using a Brix refractometer; or in the case of the two reducing sugars glucose and fructose, you can do a Fehling's titration; and there is a titration for ethanol.

The density can also be used as an index. You could also monitor the reaction with a gas pressure sensor. There are lots of other gas sensors too. Reducing sugars in wine 9.


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