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)
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.
To find the value of the expression tan(- (11pi)/6), we can use the unit circle.
1. Start by converting the given angle into radians. (- (11pi)/6)
2. The terminal point of this angle is in the 3rd quadrant, which corresponds to a reference angle of pi/6.
3. In the 3rd quadrant, the values for sine and cosine are both negative.
4. From the unit circle, we know that sin(pi/6) = 1/2 and cos(pi/6) = sqrt(3)/2.
5. Since the reference angle is positive, we need to take the negative of both sine and cosine.
6. Therefore, sin(-(pi/6)) = -1/2 and cos(-(pi/6)) = -sqrt(3)/2.
7. Using the formula tan(theta) = sin(theta) / cos(theta), we can find that tan(-(pi/6)) = (-1/2) / (-sqrt(3)/2).
8. Simplifying further, we get tan(-(pi/6)) = 1 / sqrt(3).
9. Since sqrt(3) can't be simplified, the final value of the expression tan(- (11pi)/6) is 1 / sqrt(3).