tan210

tan210 refers to the tangent of an angle measuring 210 degrees. In trigonometry, the tangent of an angle in a right-angled triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

The angle 210 degrees is located in the third quadrant of the unit circle. The tangent function is negative in the second and fourth quadrants, and positive in the first and third quadrants. Therefore, tan210 will have a positive value.

To calculate tan210, we can use the reference angle. The reference angle for 210 degrees is 210 - 180 = 30 degrees. The tangent of 30 degrees is 1/√3 or √3/3. Since 210 degrees is in the third quadrant where tangent is positive, tan210 is equal to tan30.

Thus, tan210 = 1/√3, which is approximately 0.577. This value can be confirmed using a calculator or by referring to trigonometric tables. The tangent function has a period of 180 degrees, meaning that tan(θ + 180°) = tan(θ) for any angle θ. Therefore, tan210° = tan(30° + 180°) = tan30°, reinforcing the calculated value.