Solve for x cos(3x)=-1

Problem

cos(3*x)=−1

Solution

1. Identify the general solution for the cosine function when it equals −1 The cosine of an angle is −1 when the angle is an odd multiple of π

cos(θ)=−1⇒θ=π+2*k*π

where k is any integer (k∈ℤ.

2. Substitute the argument of the cosine function, which is 3*x into the general solution formula.

3*x=π+2*k*π

3. Isolate the variable x by dividing both sides of the equation by 3

x=(π+2*k*π)/3

4. Simplify the expression to represent the general solution for x

x=(π*(1+2*k))/3

Final Answer

cos(3*x)=−1⇒x=((2*k+1)*π)/3,k∈ℤ

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