# How to calculate sine cosine and tangent without a calculator

## Sine, Cosine and Tangent 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)? 