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Trigonometry is the study of angles and [[triangle]]s, relying heavily on three basic functions: sine, cosine and tangent. These functions are abbreviated as "sin", "cos" and "tan".
'''Trigonometry''' is the study of angles and [[triangle]]s, relying heavily on three basic functions: [[sine]], [[cosine]] and [[tangent]], and their inverses, [[Cotangent]] (Cot), [[Secant]] (sec) and [[Cosecant]] (csc). These functions are abbreviated as "sin", "cos" and "tan".
These functions are defined by reference to a "right triangle," which is a triangle in which one angle is 90 degrees.
These functions are defined by reference to a "right triangle," which is a triangle in which one angle is 90 degrees.
[[Image:Right triangle.PNG|right|A right triangle]]A way to remember the relationships is the mnemonic SOH-CAH-TOA ("soak a toe"). Think of a man soaking his toe in a tub of water - preferably a three-sided tub!
[[Image:Right triangle.PNG|right|A right triangle]]A way to remember the relationships is the mnemonic SOH-CAH-TOA ("soak a toe"). Think of a man soaking his toe in a tub of water - preferably a three-sided tub!
*Sine: opposite over hypotenuse
*SOH: Sine = opposite over hypotenuse
*Cosine: adjacent over hypotenuse
*CAH: Cosine = adjacent over hypotenuse
*Tangent: opposite over adjacent
*TOA: Tangent = opposite over adjacent
==Formulas==
Complementary formulas:
:<math>\sin(90^\circ-\alpha) \, = \, \cos\alpha</math>
:<math>\cos(90^\circ-\alpha) \, = \, \sin\alpha</math>
Pythagorean trigonometric identity:
:<math>\sin^2\alpha + \cos^2\alpha \, = 1</math>
==External links==
==External links==
*[http://id.mind.net/~zona/mmts/trigonometryRealms/introduction/rightTriangle/trigRightTriangle.html Trigonometry and Right Triangles]
*[http://id.mind.net/~zona/mmts/trigonometryRealms/introduction/rightTriangle/trigRightTriangle.html Trigonometry and Right Triangles]
[[Category:Mathematics]]
[[Category:Trigonometry]]