Find the areas bounded by 4 equations

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    Areas Bounded
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SUMMARY

The discussion focuses on finding the intersection points of the equations y=cos(x) and y=sin(2x). The user successfully identifies one intersection point at x=π/2, but seeks assistance in determining the second intersection point, approximately at x=0.53. The user applies the double angle formula for sine, sin(2x) = 2sin(x)cos(x), to facilitate the calculations. The discussion highlights the importance of understanding trigonometric identities and their applications in solving intersection problems.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with the double angle formula for sine: sin(2x) = 2sin(x)cos(x).
  • Knowledge of solving equations involving trigonometric identities.
  • Ability to graph trigonometric functions to visualize intersections.
NEXT STEPS
  • Study the properties of trigonometric functions to better understand their intersections.
  • Learn how to apply the double angle formulas in various trigonometric equations.
  • Explore numerical methods for finding roots of equations, such as the Newton-Raphson method.
  • Investigate graphing tools or software to visualize intersections of trigonometric functions.
USEFUL FOR

Students studying trigonometry, mathematics educators, and anyone involved in solving equations involving trigonometric functions.

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Homework Statement


I won't post the entire problem since I'm only stuck on one part of it. I need to find where y=cos x and y=sin 2x intersect.


Homework Equations


sin(x)=cos(x +- pi/2)

6_1_21.gif


The Attempt at a Solution



cos x = sin 2x

since sin(x)=cos(x +- pi/2), sin 2x = sin(x+pi/2), therefore, 2x=x+pi/2. This gives me 1/2 pi, which is 1 of the intersection points. And of course, any point 2pi away from this is another intersection point. But how do I find the other intersection point? The one that the graph shows to be at about 0.53.
 
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sin2x =2sinxcosx (Double angle formula)
 

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