Find exact value of inverse trig functions calculator

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Find exact value of inverse trig functions calculator

By: Charlotte Johnson Updated September 26, 2017 Scientific calculators possess a number of functions that aren't usually found on standard calculators. One such function is the "Power" button. This button allows you to raise a number to a certain exponential value in a few keystrokes. This is much quicker and easier than using a standard calculator to multiply the number by itself multiple times. Enter a number in the scientific calculator. Press the "Power" button, which is marked with a ^ symbol. Key in the value of the exponent. Read the display for the answer. For instance, if you want to find the result of 9 to the third power (or "9 cubed"), press 9 followed by ^ and 3. The display should read 729. Economists and manufacturers study demand functions to see the effects of different prices on the demand for a product or service. To calculate it, you need at least two data pairs that show how many units are bought at a particular price. In its simplest form, the demand function is a straight line. Manufacturers interested in maximizing revenues use the function to help set production levels that yield the most profits. Pair the amount of sales to the selling price. For example, a blueberry farmer might sell 10 quarts at Market 1 at $2.50 each and 5 quarts at Market 2 at $3.75 each. The two ordered data pairs are (10 quarts, $2.50 per quart) and (5 quarts, $3.75 per quart). Calculate the slope of the line connecting the data points as they would lie on a graph of price versus sales. In this example, the slope is the change in price divided by the change in quantity sold, in which the numerator is ($2.50 minus $3.75) and the denominator is (10 quarts minus 5 quarts). The resulting slope is $-1.25/5 quarts, or $-0.25 per quart. In other words, for every 25-cent increase in price, the farmer expects to sell one less quart. Derive the demand function, which sets the price equal to the slope times the number of units plus the price at which no product will sell, which is called the y-intercept, or "b." The demand function has the form y = mx + b, where "y" is the price, "m" is the slope and "x" is the quantity sold. In the example, the demand function sets the price of a quart of blueberries to be y = (-0.25x) + b. Plug one ordered data pair into the equation y = mx + b and solve for b, the price just high enough to eliminate any sales. In the example, using the first ordered pair gives $2.50 = -0.25(10 quarts) + b. The solution is b = $5, making the demand function y = -0.25x + $5. Apply the demand function. If the farmer wants to sell 7 quarts of blueberries at each market, she figures the price equal to ($-0.25)(7 quarts) + $5, or $3.25 per quart. Tips You can calculate more sophisticated versions of the demand curve by using more data and running a linear regression, which produces a slope that best fits the data. You might find the relationship between price and demand is not a straight line, but is best described by a curve. Warnings The example is idealized and, in reality, it might be difficult for a manufacturer to test the effects of different prices on demand. One strategy is to label the same product with different brand names that sell at different price points. Producers of commodities, such as foods, metals, oil or nails, might be able to collect competitor data to help figure the demand function. On this page is a present value calculator, sometimes abbreviated as a PV Calculator. Present value is an estimate of the current sum needed to equal some future target amount to account for various risks. Using the present value formula (or a tool like ours), you can model the value of future money.Using the Present Value CalculatorFuture Amount ? The amount you'll either receive or would like to have at the end of the periodInterest Rate Per Year (Discount Rate) ? The annual percentage rate investment return you'd earn over the period of your investmentNumber of Years ? The total number of years until the future sum is received, or the total number of years until you need a future sum. (You can enter fractional years, such as 6.5)Present Value ($) ? The amount the future sum is worth today with the assumptions in the input fieldsThe Present Value FormulaThe general solution comes in this formula:The present value formula for annual (or any period, really) interest.where:C = Future sumi = Interest rate (where '1' is 100%)n= number of periodsExample Using the Present Value FormulaIn the simplest case, let's say you're an excellent investor and can get a 10% return on your money. You have $100 today, and you stay invested for three years:Start: $100Year 1: $1102: $1213: $133.10If I asked you for $100 today, promising to give you $120 at year three... I'd hope you'd turn that down. The present value of $120 in three years, if you have alternatives that earn 10%, is actually $90.16.That is to say, the present value of $120 if your timeframe is 3 years and your discount rate is 10% is $90.16.For the above problem, your sum would be $133.10. Here's how the math works out:Inputs: $133.10 in 3 years given 10% investment returnsPV = 133.10 / (1+.1)^3 = 133.10 / 1.1^3= 133.10 / 1.331PV = $100.00and for my generous offer of $120:Inputs: $120.00 in 3 years given you could get 10% investment returns elsewherePV = 120 / (1+.1)^3 = $90.16I hope you'd agree now. If you can make 10% a year you should turn down my offer of $120 in three years for $100 today.Why is present value important?Future quantities deal with both inflationary (or deflationary) pressures, opportunity costs, and other risks to the value of your final sum. The actual equivalent value of a sum in the future is (almost) never the same amount as having a lump sum today.That's where 'Present Value' comes into play.If you have a return estimate for what you could earn with a lump sum investment today, you can easily estimate what that future value is worth. Alternatively, present value also tells you the amount you would need to invest today if you needed to end up with the final lump sum assuming a given return... just know that forecasting of this sort is never better than an educated guess!Using the Present Value Formula and Calculator to Value Investments and TradeoffsWhile we're insinuating that 10% is an unreasonable discount rate, there will always be tradeoffs when you're dealing with uncertainty and sums in the future.For a real-life investment measure, take a look at our Dow Jones Return Calculator.After dividends and inflation are factored in, you would have seen about a 10% return, ignoring taxes and fees, since the Dow Jones Industrial Average has existed. (Remember, only adjust for inflation if you also adjust the final amount for inflation as well!) We're not sure if that's an accurate return estimate going forward, so please form your own estimate.Regardless of your number, when you forego money today, you're giving something up in the future. That's true even if you're only able to make 1% on your money reliably.And, yes, sometimes it's possible that a return of capital may be more important than a return on capital. In that sort of scenario money in the future would be worth more than today.When should you use present value estimates?Present value estimates are useful for evaluating job offers.DQYDJOther than while evaluating investments, present value estimates are useful for evaluating job offers.Many of you readers are in industries which have some sort of equity or variable compensation in your annual income. Any honest accounting of an offer evaluates your compensation other than salary, such as stock, options, or bonuses with some sort of a present value calculation (Total Compensation).Bonuses are first to go in a recession, options can go to zero (especially in early stage companies) and stock can go up, down.. or even to zero.Future values are actually a range of possible values... some of them zero. Every dollar of current salary is more valuable than variable compensation... although it doesn't have the upside of variable pay, it is safer than other income forms. When using the present value calculator you can adjust for that uncertainty by reducing the amount of future value and running the numbers again.We hope you enjoyed this brief look at evaluating investments using the present value formula. Keep this concept in mind whenever you evaluate your options going forward.What other calculators do you have?Try our other financial basics and valuation calculators:See all our financial calculators here. Good nutrition is essential for both the mind and body, but most Americans don't follow a healthy diet. That's where the daily value system comes in.The US Food and Drug Administration (FDA) created the daily value system to make it easier for people to meet their daily nutritional needs. Found on the nutrition label, the daily value system tells you can help you determine if a product is high or low in particular nutrients. What does daily value mean? Daily value (DV) refers to how much of a nutrient you should consume each day based on a 2,000 calorie diet. You can find daily values for a range of nutrients on the FDA's website. Related How many calories you should eat a day whether you're trying to maintain, lose, or gain weight The FDA chose 2,000 calories based on the energy needs of an average adult. However, this value varies based on a variety of factors like age, weight, height, and physical activity level. "[The FDA] try to keep it simple, and don't consider the individual weight of a person or if someone is an athlete, or pregnant ... it's just meant to be a baseline," says Eleana Kaidanian, a registered dietitian with her own practice. Another separate measurement, called percent daily value, is found in a separate column on the Nutrition Facts label to the right of each nutrient. These values -- listed as percents -- refer to how much of a particular nutrient you get in one serving.For example, if the percent daily value on a package of nuts says 6% protein, that means one serving of the nuts will provide you with 6% of your FDA recommended protein intake based on a 2,000 calorie diet. If you doubled the amount you ate and consumed two servings, then you'd also double your daily value to 12% of your protein requirement. How is daily value calculated? There's one clear caveat to the daily value system: Not everyone follows a 2,000 calorie diet. Fortunately, you can easily calculate your specific daily values with some simple math says Amy Lee, MD, the Chief Medical Officer at Lindora Clinic weight loss center.Let's say you follow a 1,500 calorie diet and want to convert the 2,000 calorie daily values to the equivalent for your diet. Then you should: For example: If you want to determine the daily value for protein based on a 1,500 calorie diet, you would multiply 50 grams (the daily value for protein-based off of a 2,000 calorie diet) by 1500, and then divide that number by 2000. This would get you 37.5 grams. You can also use the amount of a particular nutrient listed on food products to determine the percent daily value for different calorie diets. Divide the amount of a nutrient in a food by the value determined in the above formula. Multiply that number by 100 to convert to a percentage. For example: Let's say you follow a 1,500 calorie diet and have determined that your daily value for protein is 37.5 grams. If you eat a serving of peanut butter with 8 grams of protein per serving and want to determine the percent daily value for your 1500 calorie diet, you can divide 8 grams by 37.5 and multiply that value by 100. This means eight grams of protein is 21.3% of your daily value. How to use daily value to make healthier choices The daily value system can help you balance your diet with the proper amount of nutrients like protein, carbohydrates, fat, vitamins, and minerals. General advice: As a rule of thumb, if something has a 5% DV or less of a nutrient, it is considered to be low, while 20% DV or more is high. The FDA recommends you choose foods higher in:And choose foods lower in: For example, let's say you're choosing a breakfast cereal and have narrowed it down to two choices. The first cereal has a percent daily value of 57% fiber and 0% saturated fat, while the second cereal has 1% fiber and 2% saturated fat. The first cereal option will help you meet your recommended daily value intake for fiber and has less saturated fat than the second cereal, according to the DV system. Insider's takeaway Found on the nutrition label, daily value and percent daily value tells us how much of a nutrient to consume or not to exceed each day. It also informs us how much of a nutrient is in one serving of food. By using the daily value system and picking products high in nutrients like fiber, protein, vitamins, and minerals and low in substances like saturated fat, sodium, and sugar, you can easily fill your plate with foods that keep you feeling your best. Just know it's based off a 2,000 calorie diet so you might have to adjust according to your own calorie needs. Photo Courtesy: skynesher/E+/Getty Images Even if you consider most shopping to be a chore, shopping for a new car just might fill you with a sense of excitement instead of dread. These days, new cars -- and even recent models of used cars -- often come with some impressive bells and whistles, such as automatic braking, lane departure alerts and blind spot alerts. It can be quite a thrill to upgrade from an older car with more limited features to a shiny new model that practically drives itself (at least it feels that way). However, an unexpectedly poor trade-in value on your existing vehicle can ruin the excitement very quickly. First, an unscrupulous dealership could offer you less for your vehicle than it's actually worth to increase its own profit. Second, your car could legitimately be worth much less than you expected for any number of reasons. To avoid shock and disappointment, you need to make sure you know your car's value before you try to trade it or sell it privately. If you're not sure how to find that information, here's a quick look at some tips for calculating the value of your car. When it comes to buying and selling cars, the information out there consists of both fact and fiction. If you've heard that a brand new vehicle loses thousands of dollars in value as soon as you drive it off the lot, it's a partial truth. Once a car is registered to a new owner, it's no longer considered "new" and must be sold as a used car, no matter how few miles it was driven. This generally causes the value to drop around 10% shortly after the purchase. However, most states have buyer's remorse periods that allow new car sales to be canceled within a short period -- usually a few days -- which means the downgrade to "used" doesn't occur the minute you leave the lot. Photo Courtesy: Lane Oatey/Blue Jean Images/Getty Images According to U.S. News & World Report, depreciation for most vehicles averages about 15% to 25% per year for the first five years. Most vehicles in good condition are worth around one-third of their original purchase price at the end of the five years, but many variables can affect the value calculation for a specific car. The value of your car depends on much more than the make, model and age. The age-old claim that certain car models retain their values better than others has some truth to it. For example, in 2019, Kelley Blue Book -- a trusted auto industry resource for determining value -- reported that Toyota and Porsche were two brands that traditionally retained a high percentage of their original value for a longer period. This is partially due to higher demand for some vehicles as well as the reliability and longevity of engine parts and components. Photo Courtesy: Westend61/Getty Images Beyond market demand and the age and starting price of your vehicle, factors like mileage, condition and specific options can have a significant impact on the resale value. Make sure you know all the details about your car's exact model, including engine specs, transmission type, drivetrain, exterior trim (bumpers, headlights, wheels, etc.) and interior trim (leather, navigation, backup camera, warning and alert systems, etc.), as these features play a role in the vehicle's value. Interestingly, the role of features isn't usually to boost the value, as you might imagine. Instead, the premium features that you paid a pretty penny for when you purchased your car might do very little to improve your car's resale value. In most cases, fully-loaded vehicles with all the manufacturer's top features lose their value much more quickly than base model cars. After all, the used car market essentially dictates the value, and used car buyers are often much more focused on value and great deals than premium features. Amenities that don't hold their purchase value very well include sunroofs, premium wheels, premium seats, and turbo or supercharged engines. Photo Courtesy: Kathleen Finlay/Image Source/Getty Images The overall condition of a vehicle carries a lot of weight when it comes to determining the value. A vehicle's condition includes details about mechanical defects as well as its exterior and interior appearance. If you don't consult with a professional mechanic, determining the condition of your vehicle can be very subjective. Without knowledge of exactly what's going on under the hood or inside the vehicle's computer, many people end up believing their vehicles are in better condition than they actually are, which leads to overestimating values. Photo Courtesy: Dan LaMee/Moment/Getty Images It's much easier to account for cosmetic issues caused by dents, scratches, tears and stains. Be sure to go over your vehicle in detail and accurately note every flaw as well as anything that looks as good as new. Additionally, the odometer reading provides an instant, accurate reading for the number of miles driven, which is another important detail that influences a car's value. In general, vehicles with lower mileage have less wear and tear on their components and command higher prices than the same models with higher mileage -- assuming no other factors are dramatically different. Once you've gathered the information you need about your vehicle, you can use several online vehicle valuation tools to obtain estimates of your car's value. Many of these tools will also ask you about the location of the vehicle, as market pricing trends can vary somewhat in different parts of the country. Besides the previously mentioned Kelley Blue Book, Edmunds, NADA (National Automobile Dealers Association) and Consumer Reports have strong reputations for providing reliable pricing estimates free of charge. Photo Courtesy: Milos Bataveljic/E+/Getty Images Additionally, some large online car buying sites, like Carvana, Auto Trader and CarGurus, offer tools to help consumers determine vehicle values. However, these sites should be used with more caution, as their goal is to financially benefit by selling you a car (or buying yours) after providing the free information. One key detail that often has a huge impact on the value of your vehicle is the method you choose for selling it. Trading your used vehicle to a dealership to reduce the price of your new vehicle is easy and convenient, but it isn't usually the smartest financial choice. If you have time and another vehicle to drive before making your purchase, you can often sell your used vehicle to a private party for a higher price. Photo Courtesy: Eric Audras/PhotoAlto Agency RF Collections/Getty Images The logic is simple: A dealership can't afford to pay you the full value of the vehicle and still make a profit when they sell it as a used car. A private party, on the other hand, may be willing to pay you exactly what the vehicle is worth -- after doing their own due diligence, of course. However, if you're like many people, you prefer the minimal effort that goes into trading your used vehicle when you're ready to purchase a new one. There's nothing wrong with that as long as you don't walk onto the lot unprepared. If you want the best deal, be sure to show up armed with solid research about your car's value.

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