![]() One use for these new functions is that they can be used to find unknown side lengths and angle measures in any kind of triangle. In a right triangle you can only have acute angles, but you will see the definition extended to include other angles. The new functions will have the same values as the original functions when the input is an acute angle. ![]() You will now learn new definitions for these functions in which the domain is the set of all angles. The domain, or set of input values, of these functions is the set of angles between 0° and 90°. For example, the six trigonometric functions were originally defined in terms of right triangles because that was useful in solving real-world problems that involved right triangles, such as finding angles of elevation. (93.00 ± 0.09) x 10 6 miles (or 93.00 x 10 6 miles ± 0.Mathematicians create definitions because they have a use in solving certain kinds of problems. For the three examples given above one should write:ġ.000 ± 0.001 meters (or 1.000 meters ± 0.l%) Thus in giving the result of a measurement, one should carry enough figures to show the accuracy of the measurement, no more and no less, and should in addition state the A.D. For example, if we limit ourselves to 0.1 percent accuracy we know the length of a meter stick to 1 mm, of a bridge 1000 meters long to 1 meter, and the distance to the sun (93 million miles) to no better than 93,000 miles. The percentage uncertainty is of great importance in comparing the relative accuracy of different measurements. This is to prevent rounding errors when we convert back to absolute uncertainty. Note that it is acceptable to report relative and percent uncertainties to two figures. ![]() Fortunately there is a special notation for the percent uncertainty (%), so it will be easily recognized in writing.2.95 kg ± 4.3% Since the percent uncertainty is also a ratio of similar quantities, it also has no units. Percent Uncertainty: This is the just the relative uncertainty multiplied by 100.In fact there is no special symbol or notation for the relative uncertainty, so you must make it quite clear when you are reporting relative uncertainty.2.95 kg ± 0.043 (relative uncertainty) As a ratio of similar quantities, the relative uncertainty has no units. Relative Uncertainty: This is the simple ratio of uncertainty to the value reported.Absolute uncertainty has the same units as the value. If there is no chance of confusion we may still simply say “uncertainty” when referring to the absolute uncertainty. It is the term used when we need to distinguish this uncertainty from relative or percent uncertainties. Absolute uncertainty: This is the simple uncertainty in the value itself as we have discussed it up to now.The following list describes accepted usage. With these two new representations for uncertainty, we must be careful in speech and writing so that our audience is clear about which one is being used. The relative uncertainty can be interpreted as describing the uncertainty that would result if the measured value had been just one unit. It is simpler to compute and is given by: A similar quantity is the relative uncertainty (or fractional uncertainty). The percent uncertainty can be interpreted as describing the uncertainty that would result if the measured value had been100 units. The uncertainty of a measured value can also be presented as a percent or as a simple ratio.(the relative uncertainty).
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