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

Problem

cos(x)=−√(,3)/2

Solution

1. Identify the reference angle by finding the value of θ in the first quadrant where cos(θ)=√(,3)/2

θ=π/6

2. Determine the quadrants where the cosine function is negative. Cosine is negative in Quadrant II and Quadrant III.

3. Calculate the solution in Quadrant II using the formula x=π−θ

x=π−π/6

x=(5*π)/6

4. Calculate the solution in Quadrant III using the formula x=π+θ

x=π+π/6

x=(7*π)/6

5. Generalize the solutions to include all coterminal angles by adding 2*π*n where n is any integer.

x=(5*π)/6+2*π*n

x=(7*π)/6+2*π*n

Final Answer

cos(x)=−√(,3)/2⇒x=(5*π)/6+2*π*n,(7*π)/6+2*π*n

Want more problems? Check here!