How do you Find the Exact Value for Tan 120?

By Shivank Goel|Updated : September 5th, 2022

Tan at 120 degrees has a value of -1.7321 (approx). Tan 120 degrees is written as tan (120° /180°), which is also known as tan (2/3) or tan (2.094395....). We will talk about how to calculate tan 120 degrees with examples in this post.

Exact Value for Tan 120

The angle of 120° for tan 120 degrees is between 90° and 180°. (Second Quadrant). Due to the second quadrant's negative tangent function, the value of tan 120° is -3 or -1.7321 (approx). Given that the tangent function is periodic, we can write tan 120° as tan(120° + n 180°).

Tan 120° equals tan 300°, tan 480°, and so forth. We can find the value of tan 120 degrees by:

  • Using Unit Circle - Rotate "r" counterclockwise to establish a 120° angle with the positive x-axis to obtain the value of tan 120 degrees using the unit circle. The tan 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 (approx).
  • Using Trigonometric Functions - As cot(90° - 120°) = cot(-30°), we can utilise trigonometric identities to represent tan 120°.

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FAQs

  • Tan has a value of -1.7320508... at 120 degrees. Tan 120 degrees, also known as tan (2/3) or tan, is written as tan (120°/180°).

  • To calculate the value of tan 120 degrees using the unit circle, rotate "r" counterclockwise to create a 120° angle with the positive x-axis. At the intersection of the unit circle and r, the tan of 120 degrees equals the y-coordinate (0.866) divided by the x-coordinate (-0.5). (-0.5, 0.866). In light of this, tan 120° = y/x = -1.7321 (approx).

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