Active 10 months ago. Viewed 68k times. Lutz Lehmann k 6 6 gold badges 29 29 silver badges 94 94 bronze badges. But I'm not sure. He said it was faster than Taylor though. Since it costs less in HW, I'm pretty sure many manufacturers of cheap calculators might use it. Add a comment. Active Oldest Votes. Rajdeep Sindhu 1, 5 5 silver badges 17 17 bronze badges. George V. Williams George V. Williams 4, 2 2 gold badges 21 21 silver badges 48 48 bronze badges.
So it does actually "make" a triangle in order to find these lengths out. What is interesting is that no matter how complicated or advanced a concept in mathematics can be, at its very core, it is still likely a bunch of arithmetic. Leo has 10 years of teaching experience with students from age 3 to adults. He wants his students to leave not just memorized equations or steps but also having understood the mechanics involved.
The AC team has just finished off another successful period in which students gained acceptance to schools such as Columbia, Yale, UChicago, and more! Check out our latest Admissions Results! By Leo Lam Published on 3rd September, There are two things that we should note about this equation: To find sine, we actually have to work with a polynomial, and This polynomial is infinite.
A calculator will only estimate an answer, so the more sophisticated our calculator is, the more decimal places it will be able to display. For those of us who are unfamiliar with the exclamation mark used in this equation, I have another blog about the factorial function. Sign up for a lesson with Leo now!
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Active Oldest Votes. One of the most common algorithms for this is to take first few terms of Taylor series for sine.
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Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. But what about your pocket or scientific calculator, or, for that matter, your TI graphing calculator — where adding that architecture would be an expensive hassle? By itself, this eliminates the need to store an immense table—roughly speaking, each new smaller rotation refines the result to an additional binary digit of accuracy, and all that needs to be stored are the instructions for rotating by that angle.
Indeed, similar methods were used for those hand-generated tables: the method described so far is a geometric perspective on using the angle-sum trigonometric identities. It adds in two crucial details that computers just adore :. Both of these refinements to the scheme would seem to make our lives more difficult; after all, we lose both the nice rational angles and the hypotenuse that stays obligingly fixed at length 1. We shall see, however, that the actual computations are more straightforward, and are even simpler in binary arithmetic.
The change in the side lengths will always be given by that little triangle, which — as its sides are constructed parallel to those of the original triangle — will always be similar to the original triangle, with its scale determined by the tangent ratio of the new triangle in the fan.
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