I. Graphs of Trig Functions   

• Graphing the tangent and secant functions
• Visualizing identities
• Visualizing solving equalities

II. Is this an identity? or can you estimate a solution for the equation?

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• Tools for Winplot used in this lab:

• Equation menu
• explicit
• point
• segment
• line
  
• Animation menu
  
• Families on Inventory.
• Two
• Intersections...
• 
  
• View ... grid.... pi on scales
  

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I.Graphs of Trig Functions

• Graphing the tangent and secant functions
• The graphs of tangent and secant:
• Use implicit to graph the equation xx + yy = 1
• Plot the point (cos(h), sin(h))
• Draw  segment (0,0) to (cos(h),sin(h))
• Plot the point (1, tan(h) )
  
• Draw  segment (0,0) to (1,tan(h))
• Draw line : x=1  [ (1)x + (0)y = 1 ]
  
• use family for h.
  
• define and undefine.
  
• Change scales on X axis to show "pi".
• Plot the point (h, tan(h))
  
• use animation
• use family
• Plot graphs with explicit for
  
• y = tan(x)
• Draw line x = pi/2  [ (1)x + (0)y = pi/2 ]
  
• Plot the point (h, sec(h))
• use animation
• use family
• y = sec(x)
• Notice period for tangent and secant.
  
• Notice asymptotes for tangent and secant.
  
• Visualizing identities and Visualizing solving equations.
• Examine and comment: For which x are these functions are equal?
      *  cos(x) tan(x) ;  sin(x)
      *  cos(2x) ;  (cos(x))^2 - (sin(x))^2
      *  1 + (cot(x))^2;  (csc(x))^2
      * sin(x);  cos(x).
      * cos(x);  x.
       
  

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II. Record your answers for the next work and submit them on Moodle by Wednesday, October 10th.

For each of the following equations, use winplot to explore whether it is an identity or not. If not, find estimates for all solutions in the interval [-5, 5]

1.    sin(2x)  =  2*sin(x)*cos(x)
2.  cos(2x)  =  2(cos(x))^2 - 1
   
3.  sin(x)*tan(x) = cos(x).
4.  cos(x) = 4 - x^2
   

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