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

In summary, the conversation discusses how to find the points of intersection between the functions y=sin x and y=cos 2x for values of x between 0 and pi. The solution involves using identities for sin and cos, and graphing the functions can also be helpful. The correct points of intersection are at x=pi/2 and x=30 degrees.
  • #1
linuxux
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0

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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  • #2
It should help you. And the identities regarding the sin and cos functions should help you more...
 
  • #3
Particularly an indentity that says cos(2x) is equal to something.
 
  • #4
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...
 
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  • #6
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.
 
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1. How do you determine the point of intersection of sine and cosine?

The easiest way to determine the point of intersection between sine and cosine is by graphing both functions on the same coordinate plane and finding the coordinates of the point where the two curves intersect. Alternatively, you can use algebraic methods to solve the equations for sine and cosine simultaneously to find the point of intersection.

2. Can you use the unit circle to find the point of intersection of sine and cosine?

Yes, the unit circle can be used to find the point of intersection of sine and cosine. The coordinates of the point of intersection can be determined by finding the angles where the sine and cosine values are equal, and then using the corresponding x and y coordinates on the unit circle.

3. Is there a formula for finding the point of intersection of sine and cosine?

Yes, there is a formula for finding the point of intersection of sine and cosine. It is given by (x,y) = (cos-1t, sin-1t), where t is the value of the angle at which the two functions intersect.

4. Are there any special cases where sine and cosine do not intersect?

Yes, there are special cases where sine and cosine do not intersect. This occurs when the amplitude and period of the two functions are different. In such cases, the two curves may never intersect or may intersect at multiple points.

5. Can the point of intersection of sine and cosine be negative?

Yes, the point of intersection of sine and cosine can be negative. This occurs when the two curves intersect in the third or fourth quadrant of the coordinate plane. The coordinates of the point of intersection will be negative for both the x and y values in this case.

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