Friday, May 11, 2007

Trigonometry - Secant, Cosecant, Cotangent

In addition to the three basic trig functions we've already looked at (Sine, Cosine, Tangent), there are three other related functions. These are Secant, Cosecant, and Cotangent. These functions have similar meanings as the first three, in that they represent the ratios of various side lengths of a right angle triangle, and can be used to find angles or unknown side lengths. I will not go into extensive detail on these functions, as they are less commonly required, but I will show you what they mean.  Please remember to click on the Like button if this is helpful, and at the end, please hit the +1 button as well.

So far, with the help of SOHCAHTOA, we have seen that:

Sine = opposite / hypotenuse
Cosine = adjacent / hypotenuse
Tangent = opposite / adjacent

These new functions are related to the originals because they represent the inverse ratios.

Cosecant = hypotenuse / opposite... (compare to Sine)
Secant = hypotenuse / adjacent....... (compare to Cosine)
Cotangent = adjacent / opposite...... (compare to Tangent)

Also, these functions can be abbreviated: Cosecant = Csc, Secant = Sec, Cotangent = Cot.

At the middle school and high school math level, you will rarely have a need to use these functions, but it is good for you to know what they are. However, most trig problems at this stage can easily be solved with the original three functions.  Just in case, though, it's always good to know all the trig functions: sine, cosine, tangent, secant, cosecant, cotangent.

Please remember to Like and +1 this post if you found it helpful!  Thanks!


  1. very very helpful. THANKS!!! :D

  2. Thank you so much!

    Other than the SOHCAHTOA method, my teacher made us say "Oscar Has A Heap Of Apples, Sine, Cosine Tangent" Oscar Has refers to Opposite and Hypotenuse (sine) and so forth
    A/Apples=adjacent Heap/Has=Hypotenuse Oscar/Of=Opposite

  3. That's another great memory trick. I've never seen that one! Thanks for the post!

  4. My teacher taught me "The Cat Sat On An Orange And Had Hat" it doesn't have any meaning but it helped me remember the rules all way through high school :D

  5. My teacher taught me that SOHCAHTOA meant, "Some old hippie caught another hippie tripping on acid."

  6. My math teacher uses 'Some Old Hippie Caught Another Hippie Tripping On Acid'

  7. Helpful! :D Thanks ^^

  8. my teacher told me its like " Some People Have Curly Brown Hair Through Proper Brush"

    S= SIN
    C= COS
    T= TAN

  9. this is really useful! you taught it well thank you :)

  10. Another way to remember SohCahToa:
    "One old hippie caught another hippie tripping on acid."
    It's funny enough to help me pass trig.

  11. Do you maybe mean "Some old hippie..." :) I've never heard that one but it also seems like a good way to help remember the trig functions!

  12. Yeah I would agree that SOHCAHTOA is a really good way to help!

  13. It says that You dont need it in Highschool much.... This my teachers clearly disagree with
    An eacy way to remember a coresspondance between them is:
    -Sec= 1/cos
    -Csc= 1/sin
    -Cot= 1/tan
    I always found this more helpful in simplifying than opposite over whatever...


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