ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Basic trigonometry

Updated on May 30, 2010

Soak a What?

Sine is opposite over hypotenuse; Cosine is adjacent over hypotenuse; Tangent is opposite over hypotenuse.............or "soh cah toa" I am not a big fan of this memory enhancer but this is what is being taught and it works.

So what does this mean?

Lets look at sine first and we will just call this sin θ. This will be used to solve various components of right triangles. (Now, of course trigonometry is not just for right triangles but that is where we will start.)

If we have a triangle with an angle θ, then the operation sin θ=(opposite leg)/hypotenuse. If we let the opposite =4 cm and the hypotenuse=5 cm, then sin θ=4/5 or .8.

Okay not too bad right?

Cosine or cos θ=(adjacent leg)/hypotenuse. We know by the Pythagorean theorem (or if we know our special triangles) that the adjacent leg = 3 cm. (hyp^2-opp^2)^1/2=adj. Therefore cos θ= 3/5 or .6.

Now tangent or tan θ =(opposite leg)/ (adjacent leg)=4/3 or 1.33.

By knowing sin θ, we were able to determine both cos θ and tan θ.

Lets do one more. We have a right triangle and the tan θ=2. This means we can let the opposite leg = 2 and the adjacent leg =1 and the hypotenuse would equal (1^2+2^2)^1/2=(1+4)^1/2=5^1/2=2.24. This is all just a ratio so we could have let the opposite=4 and the adjacent=2 and the hypotenuse=4.48 but 2 and 1 respectively are a little easier to use.

sin θ=opp/hyp=2/2.24=.89
cos θ=adj/hyp=1/2.24=.45

If you have a triangle and know either sin θ, cos θ, or tan θ, you can figure out the other 2.

This is a very basic discussion of trigonometry. Trigonometry as it applies to right triangles is a relationship between angles and lengths of sides. This can be used in construction like figuring cutting angles for trusses on a slopped roof. One can figure ballistics of a projectile and this gives us a horizontal and vertical component. Trigonometry is actually a very useful math methodology.

In the next basic trigonometry post, I am going to explain how lengths of sides and angles relate to each other. I would love to hear your comments and I hope that I am explaining this in a way that most people can understand. I would love to help anyone who would like to learn math. That is my intent.

Before I end this post, I will give the other three trigonometry functions. The first three explain every side of a triangle but the following functions find their use in both proofs as well as calculus solutions so it is good to know and they are easy to learn.

Secant or sec θ=hyp/adj=1/cos θ.

Cosecant or csc θ=hyp/opp=1/sin θ.

Cotangent or cot θ= adj/hyp=1/tan θ.

sha cho cah?  Hey that doesn't sound to good.

Post note: All numbers are rounded to 2 significant digits.


    0 of 8192 characters used
    Post Comment

    • Ben Evans profile imageAUTHOR

      Ben Evans 

      8 years ago


      You are very welcome. I appreciate you stopping by to read. Where in the Philippines do you live?

    • profile image


      8 years ago

      HEY...godd job...about that nice thougth and tirck you have....tanxx a lot....and more power to you..

      JEzreel from philippines

    • Ben Evans profile imageAUTHOR

      Ben Evans 

      8 years ago

      Hey thank you for stopping and reading Romper. I am glad that you learned something.

    • romper20 profile image


      8 years ago from California

      wow nice hub!

      I think i actually learned something from it.

      Thank you,

      Romper20 :)


    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)