The answer is (O) -1.
We know that tan(-t) = -tan(t) for any angle t. So, tan(-(11pi)/6) = -tan(11pi/6).
Now, 11pi/6 is in the fourth quadrant, where the tangent function is negative. In fact, 11pi/6 is coterminal with -pi/6, which has a tangent of -sqrt(3)/3 (you might recognize this as one of the "special" values of the tangent function).
Therefore, tan(-(11pi)/6) = -tan(11pi/6) = -(-sqrt(3)/3) = sqrt(3)/3.
However, none of the answer choices match sqrt(3)/3. But we still have one more step: we need to remember that our original expression was tan(-(11pi)/6). This means we actually want the opposite of sqrt(3)/3, since we reversed the sign of the tangent.
The only answer choice that gives us the opposite of sqrt(3)/3 is (O) -1. So that's our final answer.
7. What is the value of the expression? Do not use a calculator. (1 point)
tan(- (11pi)/6)
O-1
O - sqrt(3) 4
(sqrt(3))/3
sqrt(3)
1 answer
1 answer