Find the exact value of the expression, if possible. Do not use a calculator. cos^-1[cos(-(pi )/(6))] (5pi )/(6) (pi )/(6) -(pi )/(6) (7pi )/(6)

To find the exact value of the expression , we need to understand the properties of the inverse cosine function.The inverse cosine function, denoted as or , returns the angle whose cosine is equal to . In other words, if , then .Now, let's analyze the given expression: We know that the cosine function is an even function, which means that . Therefore, we can rewrite the expression as: Since is a positive value, the inverse cosine function will return the angle whose cosine is equal to . This angle is .Therefore, the exact value of the expression is .So, the correct answer is .