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Solving Trig Equations

Here's another one:

Solve cos( 2 * theta ) + cos( theta ) = 0
We need to ditch this!  Replace it with cosines since we have another cosine!

cos( 2 * theta ) = 2 cos^2( theta ) - 1


2 cos^2( theta ) - 1 + cos( theta ) = 0 ... 2 cos^2( theta ) + cos( theta ) - 1 = 0 ... ( 2 cos( theta ) - 1 )( cos( theta ) - 1 ) = 0
 

2 cos( theta ) - 1 = 0 or cos( theta ) + 1 = 0
cos( theta ) = ( 1 / 2 )
short, positive
or
cos( theta ) = -1
 
back and forth, short, positive ... pi / 3 ... ( 4 * pi ) / 3 pi is at 180 degrees on the unit circle

theta = pi / 3 or theta = pi or theta = 4 * pi / 3

 

YOUR TURN:

 
Find all solutions: sin( 2 * theta ) - cos( theta ) = 0