Difference between revisions of "Trigonometry"
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| − | Trigonometry is the study of angles and [[triangle]]s, relying heavily on three basic functions: sine, cosine and tangent. | + | '''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 | + | *SOH: Sine = opposite over hypotenuse |
| − | *Cosine | + | *CAH: Cosine = adjacent over hypotenuse |
| − | *Tangent | + | *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]] | ||
Latest revision as of 20:47, July 13, 2016
Trigonometry is the study of angles and triangles, 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.
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!
- SOH: Sine = opposite over hypotenuse
- CAH: Cosine = adjacent over hypotenuse
- 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>