Solve for x cos(2x)=-( square root of 3)/2

Problem

cos(2*x)=−√(,3)/2

Solution

1. Identify the reference angle for the cosine function. We know that cos(θ)=√(,3)/2 when the reference angle is π/6

2. Determine the quadrants where the cosine is negative. The cosine function is negative in the second and third quadrants.

3. Set up the equations for the general solution of the angle 2*x based on the unit circle.

2*x=π−π/6+2*π*n

2*x=π+π/6+2*π*n

4. Simplify the expressions for 2*x by finding a common denominator.

2*x=(5*π)/6+2*π*n

2*x=(7*π)/6+2*π*n

5. Solve for x by dividing every term in both equations by 2

x=(5*π)/12+π*n

x=(7*π)/12+π*n

Final Answer

cos(2*x)=−√(,3)/2⇒x=(5*π)/12+π*n,(7*π)/12+π*n

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