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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 that is 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 hypotenuse.
Sine, Cosine and Tangent (often shortened to sin, cos and tan) are each a ratio of sides of a right angled triangle: For a given angle θ each ratio stays the same. no matter how big or small the triangle is. To calculate them: Divide the length of one side by another side. Example: What is the sine of 35°?
We then define the cosine and sine of the arc \(t\) as the \(x\) and \(y\) coordinates of the point \(P\), so that \(P(t) = (\cos(t), sin(t))\) (we abbreviate the cosine as \(\cos\) and the sine as \(\sin\)). So the cosine and sine values are determined by the arc \(t\) and the cosine and sine are functions of the arc \(t\). Since the arc lies ...
The main functions in trigonometry are Sine, Cosine and Tangent. They are simply one side of a right-angled triangle divided by another. For any angle " θ ": (Sine, Cosine and Tangent are often abbreviated to sin, cos and tan.)
This page explains the sine, cosine, tangent ratio, gives on an overview of their range of values and provides practice problems on identifying the sides that are opposite and adjacent to a given angle. The Sine, Cosine and Tangent functions express the ratios of sides of a right triangle.
The three trigonometric ratios; sine, cosine and tangent are used to calculate angles and lengths in right-angled triangles. The sine and cosine rules calculate lengths and angles in any...
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.
