What is the value of tan 0°?

What is the value of tan 0°?

• A. 0
• B. 1
• C. undefined
• D. -1

Answer: (A)

The value of tan 0° equals 0 because the tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. When the angle is 0°, the length of the opposite side is 0 while the length of the adjacent side remains non-zero. Therefore, the tangent at this angle can be calculated as: \[ \tan(0°) = \frac{\text{opposite}}{\text{adjacent}} = \frac{0}{\text{non-zero}} = 0. \] This is consistent within the unit circle as well, where the coordinates at 0° (or 0 radians) are (1, 0). The tangent, which is the sine (y-coordinate) divided by the cosine (x-coordinate), also confirms this: \[ \tan(0°) = \frac{\sin(0°)}{\cos(0°)} = \frac{0}{1} = 0. \] Thus, the correct answer reflects the fundamental understanding of the tangent function in trigonometry.

The value of tan 0° equals 0 because the tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle. When the angle is 0°, the length of the opposite side is 0 while the length of the adjacent side remains non-zero. Therefore, the tangent at this angle can be calculated as:

[

\tan(0°) = \frac{\text{opposite}}{\text{adjacent}} = \frac{0}{\text{non-zero}} = 0.

]

This is consistent within the unit circle as well, where the coordinates at 0° (or 0 radians) are (1, 0). The tangent, which is the sine (y-coordinate) divided by the cosine (x-coordinate), also confirms this:

[

\tan(0°) = \frac{\sin(0°)}{\cos(0°)} = \frac{0}{1} = 0.

]

Thus, the correct answer reflects the fundamental understanding of the tangent function in trigonometry.