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Practice Lesson 7.7

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					                        Practice Lesson 7.7
Solving Trig Equations

Some solutions go well beyond inverse relations so be careful!!!

Solve for x on the interval [0,2 ]

2sin2 x  1  0




  3 cot x  1  0




           
cos(2x        )  1
           2




Solve each and give a general formula for all solutions

      x
tan      1
      2




sec2x  2
                Practice Lesson 7.7: Solutions
Solving Trig Equations

Some solutions go well beyond inverse relations so be careful!!!

Solve for x on the interval [0,2 ]

2sin2 x  1  0

      1
sin x  
       2
   3 5 7
x , , ,
  4 4 4 4


  3 cot x  1  0

            1
cot x  
             3
      2 5
x      ,
       3 3

            
cos(2x      )  1
           2
cos( )  1 means   
                     
That leads to 2x          and
                     2
      3
x
       4

Graph the original equation (set your window properly) and see if there are
other solutions.
Hmmmmm…. x = what else? Why?

Solve each and give a general formula for all solutions

      x
tan      1
      2
x           
    ,x  
2    4       2
                          
General formula: x             k, k is an integer… not sure, check it by graphing
                           2
sec2x  2
     2      
2x     ,x 
      3      3
                                          2
General Formula: x          k and x         k where k is an integer
                       3                    3

				
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