sin(x) = sin(x + pi/3)

I know this is simple but so am i... thanks in advance for any help

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- March 1st 2010, 11:32 AMjsel21Need help solving for x!
sin(x) = sin(x + pi/3)

I know this is simple but so am i... thanks in advance for any help - March 1st 2010, 11:40 AMe^(i*pi)
- March 1st 2010, 03:34 PMjsel21
but there are solutions. When entering both of these in my graping calculator there are multiple points in which the two functions intersect. I just dont know how to solve for them. I'm looking for the the solutions between 0 and 2pi.

- January 26th 2011, 11:07 AMjsel21
- January 26th 2011, 11:14 AMTheEmptySet
Use the identity that

This gives the equation

Or

This will give you the solutions you want. - January 26th 2011, 05:20 PMLoblawsLawBlog
If is a solution then and must lie at the intersections of some horizontal line through the unit circle. Furthermore, the angle between these points (measured from the origin) must be . But the other angles between the rightmost point and the positive x axis and the leftmost point and the negative x axis must be equal by symmetry, so call them .

This leads to the equation , since together the three angles make a straight line. This gives you one solution and then the other is easily found. - January 30th 2011, 06:51 AMArchie Meade
Visually, you could use the Unit Circle.

gives the y co-ordinate of a point on the Unit Circle,

hence the y-axis from to acts as an axis of symmetry.

requires that and are either side of the y-axis.

The exact same logic may be used underneath the x-axis for

to obtain a 2nd solution.

Complete the analysis by adding multiples of 360 degrees to the two solutions.