Trig functions, finding co-ordinates

AI Thread Summary
To find the coordinates of the intersection point B for the functions f(x)=sin(2x) and g(x)=cos(x), the equations must be equated: sin(2x) = cos(x). The discussion highlights that the graphs intersect at multiple points within the specified domain of x in [0, 270]. A specific solution approach involves using trigonometric identities, such as sin(2x) = 2sin(x)cos(x), to simplify the equation. The known intersection point A is at (30, 0.87), but further clarification on the range of solutions is needed. The conversation emphasizes the importance of defining the domain to accurately identify all intersection points.
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Homework Statement



I have a graph with the functions f(x)=sin2x and g(x)=cosx. The 2 graphs intersect at point B. They want me to find the co-ordinates of B.

Homework Equations





The Attempt at a Solution



Must I equate the two graphs?

sin2x = cosx
2x = 90-x, 3x = 90, x=30 or 2x = 180-(90-x), x=90

It doesn't seem right, is their any other steps?
 
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Aren't you given any specific range within which you want the solution, both the graphs intersect at many points.
 
they say that f and g intersect at A(30:0.87) and B.
the domain is xE[0;270].
Thats all that is given.
 
Do you know a trig identity for sin(2x)?
 

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