How do you Find the Exact Value for Tan 120?

By BYJU'S Exam Prep

Updated on: November 9th, 2023

The exact value for Tan 120 is found using a specific formula and the resultant value is -1.7321 (approx). Tan 120 degrees is written as tan (120° /180°), which is also known as tan (2/3) or tan (2.094395….). Tan 120° equals tan 300°, tan 480°, and so forth.

Exact Value for Tan 120

The angle of 120° for Tan 120° is between 90° and 180°. (second quadrant). The value of tan 120° is -3 or -1.7321 (approximately) because of the negative tangent function of the second quadrant. Given that the tangent function is a period, we can write tan 120° as tan (120° + n 180°). We can find the value of tan 120 degrees by:

  • Using Unit Circle: Rotate “r” counterclockwise to establish a 120-degree angle with the positive x-axis to obtain a value of tan 120 degrees using the unit circle. A tandem of 120 degrees is equal to the y-coordinate (0.866) divided by the x-coordinate (-0.5) at the place where the unit circle and r cross (-0.5, 0.866). Accordingly, tan 120° = y/x = -1.7321 (approximately).
  • Using Trigonometric Functions: As cot(90° – 120°) = cot(-30°) , we can use trigonometric identities to represent tan 120°.

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