Solve for x 1=8cos(x+1)-3

Problem

1=8*cos(x+1)−3

Solution

1. Isolate the trigonometric term by adding 3 to both sides of the equation.

1+3=8*cos(x+1)

4=8*cos(x+1)

2. Divide both sides by 8 to solve for the cosine function.

4/8=cos(x+1)

1/2=cos(x+1)

3. Apply the inverse cosine function to find the general solutions for the argument x+1

x+1=arccos(1/2)+2*π*n

x+1=±π/3+2*π*n

4. Solve for x by subtracting 1 from both sides for both cases, where n is any integer.

x=−1+π/3+2*π*n

x=−1−π/3+2*π*n

Final Answer

x=−1±π/3+2*π*n

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