How to determine the point of intersection of sine and cosine?

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Homework Help Overview

The discussion revolves around finding the points of intersection between the functions y=sin x and y=cos 2x within the interval from 0 to π. Participants are exploring the mathematical relationships and identities related to these trigonometric functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss equating the two functions as a starting point and question how this approach aids in finding intersections. There is mention of relevant identities that could simplify the problem, and one participant considers graphing the functions for verification.

Discussion Status

Some participants have provided guidance regarding the use of trigonometric identities, while others express uncertainty about the number of intersection points within the specified range. Multiple interpretations of the problem are being explored, and there is a recognition of potential errors in initial attempts.

Contextual Notes

Participants are working under the constraints of the specified interval and are questioning assumptions about the nature of the intersection points, including the expectation of "nice" numbers.

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Homework Statement



Im not sure how to start this question: determine the points of intersection between [tex]y=sin x[/tex] and [tex]y=cos 2 x[/tex] for x between 0 and pi.

The Attempt at a Solution



First thing that comes to mind is the eqaute the two, but i don't know how that helps me?
 
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It should help you. And the identities regarding the sin and cos functions should help you more...
 
Particularly an indentity that says cos(2x) is equal to something.
 
thanks I've got it now, but is the only point of intersection in the range at [tex]\frac{\pi}{2}[/tex]? i suppose i could graph it to be sure...
 
Last edited:
okay, i was solving incorrectly, they will also both be at [tex]30^{o}[/tex]. i also assumed i would get a "nice" number. thanks.
 
Last edited:

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