Trig Functions and Co-functions

         There is nothing more confusing then trig, it is a well known fact. Sine, Cosine, and Tangent seem pretty easy to understand, but other functions stem from these. Now introducing Co-secant, Secant, and Cotangent. These are known as co - functions because they correspond to one of the main trig functions. Sine and Co-secant are co functions, Cosine and Secant are co - functions. And as you may have guessed Cotangent and Tangent are co - functions. Now co - functions are just 1 over the main function. for instance Cotangent is 1/tan or since tan is sin/cos it is cos/tan. Now to simplify these kinds of problems you must put everything in terms of sin and cos. For example:

csc-tan-cos

Putting everything in terms of sin and cos:

1/sin-sin/cos-cos

Now cancel out:

     Both the sin's in the numerator and denominator cancel out and you place cos over one at the end and then both cos's cancel out laving you with:

1/1

Final answer: Because one divided by one is still one your final answer is one. Simple.

      

        Now sometimes these problems are squared. These are still solved in the exact same way but is your final answer was to be cos it would become cos^2. Just make sure everything you cancel out makes sense. for example if your final answer is 1/cos that can be simplified to just sec. 

             

    Happy Trig-ing!