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In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the ...
The sine and the cosine functions, for example, are used to describe simple harmonic motion, which models many natural phenomena, such as the movement of a mass attached to a spring and, for small angles, the pendular motion of a mass hanging by a string. The sine and cosine functions are one-dimensional projections of uniform circular motion.
A geometric way of deriving the sine or cosine of 45° is by considering an isosceles right triangle with leg length 1. Since two of the angles in an isosceles triangle are equal, if the remaining angle is 90° for a right triangle, then the two equal angles are each 45°.
Signs of trigonometric functions in each quadrant. All Students Take Calculus is a mnemonic for the sign of each trigonometric functions in each quadrant of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving counterclockwise through quadrants 2 to 4.
Euler's formula states that, for any real number x, one has = + , where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted cis x ("cosine plus i sine").
An open single-cavity bullet mold and a closed two-cavity mold. A cast bullet is made by allowing molten metal to solidify in a mold.Most cast bullets are made of lead alloyed with tin and antimony; but zinc alloys have been used when lead is scarce, and may be used again in response to concerns about lead toxicity.
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This is an accepted version of this page This is the latest accepted revision, reviewed on 12 February 2025. Classified advertisements website Craigslist Inc. Logo used since 1995 Screenshot of the main page on January 26, 2008 Type of business Private Type of site Classifieds, forums Available in English, French, German, Dutch, Spanish, Italian, Portuguese Founded 1995 ; 30 years ago (1995 ...