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Sine, Cosine and Tangent. 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
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The Sine function ( sin (x) ) The sine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the opposite side to the longest side of the triangle. In the illustration below, sin (α) = a/c and sin (β) = b/c. From cos (α) = a/c follows that the sine of any angle ...
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Use this sin calculator to easily calculate the sine of an angle given in degrees or radians. The sine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the opposite side to the longest side of the triangle. Since for a right triangle the longest side is the hypotenuse and it is opposite to the right angle, the sine of a right angle is equal to the ratio of the hypotenuse to itself, thus equal to 1. You can use this sine calculator to verify this. A commonly used law in trigonometry which is trivially derived from the sine definition is the law of sines :. The sine function can be extended to any real value based on the length of a certain line segment in a unit circle circle of radius one, centered at the origin 0,0 of a Cartesian coordinate system. Other definitions express sines as infinite series or as differential equations, meaning a sine can be an arbitrary positive or negative value, or a complex number. The reciprocal of sine is the cosecant: csc x , sometimes written as cosec x , which gives the ratio of the length of the hypotenuse to the length of the side opposite to the angle. The inverse of the sine is the arcsine function: asin x or arcsin x. The arcsine function is multivalued, e. It is useful for finding an angle x when sin x is known. If the angle is known, then simply use our sine calculator which supports input in both degrees and radians. Once you have measured the angle, or looked up the plan or schematic, just input the measurement and press "calculate". This is how easy it is. If the angle itself is unknown, one way to calculate the sine is to know the measurements of the lengths of the side opposite to it as well as the hypotenuse side c in the figure. Other ways involve using the law of sines. The sine function is usually used to model periodic phenomena in physics, biology, social sciences, etc. For example sound and light waves, day length and temperature variations over the year can be represented as a sine. Above: a wave generated using the sine function. A sine wave is the mirror image of a cosine wave. If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G. Calculators Converters Randomizers Articles Search. Sine Calculator Use this sin calculator to easily calculate the sine of an angle given in degrees or radians. Share calculator:. Embed this tool! Related calculators Cosine Calculator Arcsine Calculator. Quick navigation:.
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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:. Divide the length of one side by another side. Good calculators have sin, cos and tan on them, to make it easy for you. Just put in the angle and press the button. You can read more about sohcahtoa Move the mouse around to see how different angles in radians or degrees affect sine, cosine and tangent. In this animation the hypotenuse is 1, making the Unit Circle. Notice that the adjacent side and opposite side can be positive or negative, which makes the sine, cosine and tangent change between positive and negative values also. It will help you to understand these relatively simple functions. You can also see Graphs of Sine, Cosine and Tangent. To complete the picture, there are 3 other functions where we divide one side by another, but they are not so commonly used. They are equal to 1 divided by cos , 1 divided by sin , and 1 divided by tan :. Adjacent is always next to the angle And Opposite is opposite the angle. How to remember? Think "Sohcahtoa"! It works like this: Soh And we want to know "d" the distance down.