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Section 2 - Verifying Trig Identities

Page history last edited by PBworks 16 years, 3 months ago

 

 

 

VERIFYING TRIG. FUNCTIONS

 

 

 

 

FIVE EASY TRICKS TO HELP YOU VERIFY THESE EQUATIONS:

1.  Pick the HARD side to work with (most of the time it will be the longer of the two sides)

2.  LOOK FOR IDENTITIES!!!

       -----The identities are:

                    *tanx=sinx/cosx

                    *cotx=cosx/sinx

                    *sineq=x^2 +coseq=x^2 =1

                    *1+coteq=x^2 =csceq=x^2

                    *taneq=x^2 +1=seceq=x^2

3.  Put EVERYTHING in terms of sine or cosine

4.  Factor, if you can.  

5.  Combine fractions

 

 

AN (easy) EXAMPLE TO HELP YOU:

Verify           1

                ______  = secx

                  cosx

 

 ***Ask yourself the five questions above: 

                         1. Which side is the hard side?? Since the left side is in terms of cosine, go with the right!

                         2. Are there any identities??  No, there are not!

                         3. What, on the right side, can be put into terms of sine or cosine??  secx=1/cosx

                         4. What can be factored?? Nothing!

                         5. Do we need to combine any fractions??  No, we don't!!!

 

Even though we didn't need all those steps, it helps to go through it just in case we missed something.  So, after all the hard work we did, we figured that 1/cosx=1/cosx.  But WHY you might still be asking??  Because secx= 1/cosx.  We answered that when we got to step three!!! 

 

 

MORE (harder) EXAMPLES:

 

EXAMPLE 1:

 

sinx secx= tanx

    step 1: sinx  multiplied by  1

                                           ____

                                           cosx

    step 2:   sinx       

                 _____      =   tanx!!!!

                  cosx

 

 

 

 

EXAMPLE 2:

 

sec x  +  tan x=   cosx

                          _____

                          1-sinx

 

step 1:   1                  sin x

           _____    +     ______

           cos x               cox x

 

step 2:  1- eq=sin^2x

            _________                          cosx

 

           cosx(1-sinx)                  =  ____

 

step 3:  eq=cos^2x                                1-sinx

             _____

            cosx(1-sinx)

 

 

EXAMPLE 3:

 

eq=csc^4x-2csc^2x+1=cot^4x

 

step 1:   (eq=csc^2x-1)   (eq=csc^2x-1)      =    eq=cot^4

                                                          ____

step 2:    (eq=cot^2x)(eq=cot^2x)

 

 

 

EXAMPLE 4:

 

eq=tan^2x cos^2 + cot^2x sin^2x =1

 

step 1:    eq=sin^2x           eq=cos^2x              eq=cot^2x

               _____   x     _____     +   ______    x    eq=sin^2x               =1

               eq=cos^2x              1                eq=sin^2x

 

step 2:  eq=sin^2x  +  eq=cos^2x

Comments (1)

Anonymous said

at 8:42 pm on Jan 8, 2008

The setup is great (I love the "5 easy tricks").. check example 2 - looks like you left out a couple of steps near the beginning. Also check example 4 - something's wrong there, too. 19/20

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