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°.