How to calculate sine cosine and tangent without a calculator

Sine, Cosine and Tangent

how to calculate sine cosine and tangent without a calculator

Sine, Cosine and Tangent are the main functions used in Trigonometry and are based Good calculators have sin, cos and tan on them, to make it easy for you.

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Exactly what happens when I type the sine or cos or tan etc for that matter of an angle into my calculator? I type it in and it magically gives me an answer, a number that is essentially unrelated to the angle I inputed. Is the calculator just reading off of a list created from people who used rulers to physically measure the distance on a graph or is there a mathematical function that defines it? A calculator or computer program is not reading off of a list, but is using an algorithm that gives an approximate value for the sine of a given angle. One way is to take a certain amount of terms the more terms you take, the more accurate the approximation from the Taylor series for sine:. See how closely the polynomial formed from the first four terms of the Taylor series approximates the sine curve near the origin.

Trigonometry involves calculating angles and functions of angles, such as the sine, cosine and tangent. Calculators can be handy in finding these functions because they have sin, cos and tan buttons. However, sometimes you won't be allowed to use a calculator on a homework or exam problem or you might simply not have a calculator. Don't panic! People were calculating trig functions long before calculators came along, and with a few simple tricks, so can you.

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Before getting stuck into the functions, it helps to give a name to each side of a right triangle:. Sine , Cosine and Tangent often shortened to sin , cos and tan are each a ratio of sides of a right angled triangle:.

How does the calculator find values of sine (or cosine or tangent)?

By using our site, you acknowledge that you have read and understand our Cookie Policy , Privacy Policy , and our Terms of Service. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. In school, we just started learning about trigonometry, and I was wondering: is there a way to find the sine, cosine, tangent, cosecant, secant, and cotangent of a single angle without using a calculator? Sometimes I don't feel right when I can't do things out myself and let a machine do it when I can't. In higher mathematics, we often notice that some things which are really easy to talk about but difficult to express rigorously have a property which is really easy to express rigorously but something that we probably wouldn't have thought of to begin with.

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