Finding Roots of b1 and b2 Between 0 and 30

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SUMMARY

The discussion focuses on finding the roots of two functions, b1 and b2, defined as b1:=(x/10)+sin((x/3)+(Pi/2)) and b2:=(1-2*cos((x/4)+(Pi/2)), within the interval 0 to 30 using Maple. While plotting the functions indicates two roots, the fsolve function only returns one root, specifically 12.83815087. The solution involves plotting the functions to identify root intervals and using fsolve in those specific intervals to isolate each root effectively.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Familiarity with Maple software for symbolic computation
  • Knowledge of root-finding algorithms, specifically fsolve
  • Ability to interpret graphical representations of functions
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  • Learn how to use Maple's fsolve function with specified intervals
  • Explore plotting techniques in Maple for better visualization of functions
  • Study the behavior of trigonometric functions within defined intervals
  • Investigate numerical methods for root-finding beyond fsolve
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Mathematicians, engineers, and students who are working with trigonometric functions and require assistance in finding roots using computational tools like Maple.

85David
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Ok, i got two funktions:
b1:=(x/10)+sin((x/3)+(Pi/2));
and
b2:=(1-2*cos((x/4)+(Pi/2)));

I need to determine all the roots between 0 < x > 30

If I plot the functions i see that there should be two roots
plot([b1,b2],x=0..30);

But when try to get maple to calculate the roots It only comes up with one root:
fsolve(b1=b2,x=0..30);
12.83815087

Thanks and sorry for my bad english.
 
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Plot the function and get an idea of where the roots are, then tell maple to find the roots in an interval that contains only one of the two roots. So if the roots are 5 and 15, then fsolve([b1,b2],x=0..10) and for the other one 10..30
 

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