Solve for x 2cos(x)+3=2

Problem

2*cos(x)+3=2

Solution

1. Isolate the trigonometric term by subtracting 3 from both sides of the equation.

2*cos(x)=−1

2. Divide both sides by 2 to solve for the cosine of x

cos(x)=−1/2

3. Identify the reference angle. The cosine of π/3 is 1/2 Since the value is negative, x must be in the second or third quadrant.

x=π−π/3=(2*π)/3

x=π+π/3=(4*π)/3

4. Generalize the solution by adding multiples of the period 2*π to account for all possible values of x

x=(2*π)/3+2*k*π

x=(4*π)/3+2*k*π

Final Answer

x=(2*π)/3+2*k*π,(4*π)/3+2*k*π* for any integer *k

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