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Opposite. Sine, Cosine and Tangent. The three main functions in trigonometry are Sine, Cosine and Tangent. They are just the length of one side divided by another. For a right triangle with an angle θ : Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent.
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°?
For an angle θ, the functions are calculated this way: Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent.
For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them. The reciprocal identities arise as ratios of sides in the triangles where this unit line is no longer the hypotenuse.
Sine, cosine and tangent are the primary trigonometry functions whereas cotangent, secant and cosecant are the other three functions. The trigonometric identities are based on all the six trig functions.
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.
Sine: The sine ratio for any given angle is defined as the ratio of the perpendicular to the hypotenuse. In the given triangle, sine of angle θ can be given as, sin θ = AB/AC. Cosine: The cosine ratio for any given angle is defined as the ratio of the base to the hypotenuse. In the given triangle, cosine of angle θ can be given as, cos θ = BC/AC.
