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Sine and Cosine with Algebra

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|  Updated:  
2016-03-26 10:57:05
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Trigonometry For Dummies
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You can approximate, fairly accurately, the sine and cosine of angles with an infinite series, which is the sum of the terms of some sequence, or list, of numbers. Take note, however, that the series for sine and cosine are accurate only for angles from about –90 degrees to 90 degrees.

The series for the sine of an angle is

image0.jpg

and the series for the cosine of an angle is

image1.jpg

To use these formulas, you have to write the angle measure, x, in radians and carry out the computations several places. The exclamation points in the formulas don’t mean “Oh, goodness! It’s a 3!”

The exclamation points are mathematical operations called factorials. Factorial means to multiply that number times every positive integer smaller than it.

Going back to the series for the sine, an angle of 30 degrees is about 0.5236 radians. To find sin 0.5236, use the formula to get

image2.jpg

The result is pretty close to the sine of 30 degrees, which is

image3.jpg

Carrying out the computations using a few more terms will make the result even closer to the actual answer. And the closer the angle measure is to 0, the more quickly the value of the sine or the cosine meets the exact value (the fewer terms are necessary for the answer).

About This Article

This article is from the book: 

About the book author:

Mary Jane Sterling (Peoria, Illinois) is the author of Algebra I For Dummies, Algebra Workbook For Dummies, Algebra II For Dummies, Algebra II Workbook For Dummies, and many other For Dummies books. She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.