Solve for x cos(3x)=-1/2

Problem

cos(3*x)=−1/2

Solution

1. Identify the reference angle for the cosine function. Since cos(π/3)=1/2 the reference angle is π/3

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

3. Find the general solutions for the argument 3*x using the unit circle. In the second quadrant, 3*x=π−π/3+2*k*π=(2*π)/3+2*k*π In the third quadrant, 3*x=π+π/3+2*k*π=(4*π)/3+2*k*π where k is any integer.

4. Solve for x by dividing both sides of each equation by 3

Final Answer

x=(2*π)/9+(2*k*π)/3,(4*π)/9+(2*k*π)/3

Want more problems? Check here!