sin 4x − cos 2x = 0

2sin 2x cos 2x − cos 2x = 0

Factoring gives:

cos 2x (2 sin 2x − 1) = 0


EITHER

`cos 2x= 0`

`2x=pi/2,(3pi)/2,(5pi)/2,(7pi)/2`

`x=pi/4,(3pi)/4,(5pi)/4,(7pi)/4`

OR

`sin 2x= 1/2`

`2x=pi/6,(5pi)/6,(13pi)/6,(17pi)/6`

`x=pi/12,(5pi)/12,(13pi)/12,(17pi)/12`


Or, in decimal form:

`x= 0.26, 0.79, ` `1.31, 2.36, ` `3.40, 3.93, ` `4.45, 5.50.`

The graph of `y = sin 4x− cos 2x` is as follows. We can see from where the graph cuts the x-axis that our answers are reasonable.

Graphical solution trigo equation

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