Posted by caitlyn on Tuesday, April 26, 2011 at 9:14pm.
cos2x-cosx=0
expand the left hand side
cos²(x)-sin²(x)-cos(x)=0
2cos²(x)-1 - cos(x)=0
substitute c=cos(x)
2c²-c-1=0
c=(-1±√(9))/4
=-1 or 1/2
cos(x)=-1 when x=π (0≤x≤2π)
or
cos(x)=1/2 when x=π/3 or x=5π/3 (0≤x≤2π)
Substitute each of the three solution into the original equation to make sure that the solutions are acceptable.
Reiny is right.
There was a mistake in the solution of the quadratic.
c=(1±√(9))/4
=1 or -1/2
cos(x)=1 when x=0 or 2π (0≤x≤2π)
or
cos(x)=-1/2 when x=π±π/3 (0≤x≤2π)
Substitute each of the three solution into the original equation to make sure that the solutions are acceptable.
Related Questions
Pre calc - Find solutions on interval 0,2pie (cosx/1+sinx) + (1+sinx/cosx) = -4
identities trig? - find all solutions to the equation in the interval [0,2pie] ...
Precalculus - Please help!!!!!!!!!!! Find all solutions to the equation in the ...
Pre Calc - Solve the equation on the interval [0,2pi). cos2x=(*2/2)
Pre Calc - Solve the equation on the interval [0,2pi). cos2x=(*2/2)
pre-calc - Solve: cos(2x-180) - sin(x-90)=0 my work: cos2xcos180 + sin2xsin180= ...
Pre-Calc - Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= ...
Pre-Calculus - Find all solutions to the equation in the interval [0, 2pi) cos4x...
Advanced Math - Could someone help me with those two questions. I need to know ...
Trigonometry - Solve for x in the interval 0<=x<360: 1. 2sin2x+...
For Further Reading
