What is the exact value of [tex]\tan\left(-\frac{13\pi}{6}\right)[/tex]?
Provide an explanation.
Answer (3)
The exact value of tan (-13pi/6) is equal to √3/3. This result is obtained by simplifying the angle to its equivalent within the range of 0 to 2π, and identifying it as a fourth quadrant angle with a reference angle of π/6. ;
The exact value of tan -13π/6 can be determined by understanding the properties of the tangent function and the unit circle. First, realize that the tangent function has a period of π, which means tan(θ) = tan(θ + kπ) for any integer value of k. Since -13π/6 is equivalent to -2π + π/6 after adding 2π (which is 12π/6), the angle -13π/6 corresponds to the same point on the unit circle as π/6, but in the opposite direction due to the negative sign.
Since π/6 is 30 degrees, and the tangent function is odd (meaning tan(-θ) = -tan(θ)), the value of tan(-13π/6) is the opposite of tan(π/6). The exact value of tan(π/6) is √3/3, so the exact value of tan -13π/6 is -√3/3.
The exact value of tan ( − 6 13 π ) is − 3 3 . This is achieved by simplifying the angle to its coterminal equivalent and determining its reference angle. The result utilizes the properties of the tangent function in the second quadrant.
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