How do you solve 2cos(3x + pi/4) =1?

1 Answer
A. S. Adikesavan
Jun 3, 2016

The general solution is (24n+1)pi/36 and (24n-7)pi/36, n = 0, 1, 2, 3,...,
n=0: pi/36 in (0, pi/2) and -7/36pi in (-pi/2, 0). The solution in (0, pi) are pi/36 and (25/36)pi.

Explanation:

cos(3x+pi/4)=1/2=cos(+-pi/3,) and, for the general solution,

cos(3x+pi/4)=1/2=cos(2npi+-pi/3), n=0, 1, 2, ..

So, the general solution is

3x+pi/4=2npi+-pi/3, n=0, 1, 2, ... Solving,

x=(24n+1)pi/36 and x=(24n-7)pi/36, n = 0, 1, 2, 3,...,

The solution in (0, pi) are pi/36 and (25/36)pi.

The second comes from n=1 of x=(24n+1)pi/36.

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