ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

HEXAGON: An Aid in Remembering the Eight Fundamental Trigonometric Identities

Updated on April 13, 2011

                                                              BRIEF HISTORY

      Trigonometry is one of the oldest branches of mathematics, not by name, perhaps, but in its application to the measurement of distances, heights, depths, areas, and volumes. In the early centuries, the seasons of the year and the hours of the day are indicated by shadows cast by an upright pole, tree or rock. A tree or other upright objects which casts a shadow for this purpose was called by the Greeks a gnomon (which means inspector) and the shadow was called an umbra, Latin for shadow. When the umbra is longest at  noon, thus it is called the winter solstice; whereas when shortest, it is called the summer solstice, usually occurring during the month of June.

      Other notable evidences of the use of the triangle in measurement are found in sundials used to measure or indicate the time of the day. These sundials were commonly used a few centuries ago and some are still being used in some oriental countries.

      As means of measurement, trigonometry seems to have developed very early in Asia, specifically in India, Iraq, Egypt, and China. Some traces appear about 4, 000 years ago, generally in the surveying of land, the planning of irrigation ditches and the determination of the height of edifices (as in the case of the Pyramid at Khafre, Egypt).

     As a science, it is to the Greeks, at one time the most scholarly of the ancient peoples of the Mediterranean region that trigonometry owes its origin.

     Hipparchus (about 140 B.C.) and Ptolemy about three centuries later studied not only plane but also spherical trigonometry. They knew some of our formulas including sin2a + cos2a = 1, although of course, not using the same symbols, notations and representations.

    The trigonometry which is being used now dates from the seventeenth century, stemming immediately after the Rebirth or Renaissance Period, when it was greatly improved particularly in relation to the symbols in Italy, Germany,  England, and adjacent countries.


Etymologically speaking, trigonometry comes from the Greek words:

“tri” meaning “three”

gonia meaning “angle”

metronmeaning “a measure”

Therefore, Trigonometry is the measurement of three angles or triangles.

     TRIGONOMETRY involves functions of angles in a triangle, called trigonometric functions, which depend on ratios of the sides of the triangle. Trigonometry is widely utilized in the physical sciences, particularly in navigation, astronomy, surveying and mechanics. Without climbing a mountain top, its altitude can be measured through trigonometry. Without crossing a river, its breadth can be obtained through trigonometry. Trigonometric functions are also in other fields, such as analysis of financial markets, probability theory, statistics, biology, medical imaging, computer graphics and crystallography.

From six equilateral triangles, what polygon can be formed such that one of its side is equal to that of the triangle?


Now, learn how to use the hexagon in remembering trigonometric identities...and prove these identities.


Submit a Comment
  • alphonsians93 profile image


    8 years ago from Cebu Philippines

    Hello maam!!! welcome to Hubpages!!!1 keep writing you will enjoy it!!! parehas nilang waboy aris...nalingaw pod!!! weww!!!


This website uses cookies

As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

Show Details
HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
LoginThis is necessary to sign in to the HubPages Service.
Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
AkismetThis is used to detect comment spam. (Privacy Policy)
HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
MavenThis supports the Maven widget and search functionality. (Privacy Policy)
Google AdSenseThis is an ad network. (Privacy Policy)
Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
Index ExchangeThis is an ad network. (Privacy Policy)
SovrnThis is an ad network. (Privacy Policy)
Facebook AdsThis is an ad network. (Privacy Policy)
Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
AppNexusThis is an ad network. (Privacy Policy)
OpenxThis is an ad network. (Privacy Policy)
Rubicon ProjectThis is an ad network. (Privacy Policy)
TripleLiftThis is an ad network. (Privacy Policy)
Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
ClickscoThis is a data management platform studying reader behavior (Privacy Policy)