Question

Tan(√3 ) is not equal to 30. But tan⁻¹ (1/V3) is equal to 30. Why?

a) Trigonometric identities
b) Inverse functions
c) Unit circle properties
d) Angle conversions

Answer 1

The discrepancy between tan(√3) and tan⁻¹(1/√3) results from one being the inverse operation of the other: tan(√3) is the ratio given an angle, while tan⁻¹(1/√3) is the angle given a ratio.

Step-by-step explanation:

The question you are asking relates to the trigonometric function tangent (tan) and its inverse (tan⁻¹ or arctan). When you calculate tan(√3), you are looking for the ratio of the opposite side to the adjacent side of a right triangle with an angle whose tangent ratio equals √3, which is not 30 degrees. However, when you take tan⁻¹ (1/√3), you are trying to find the angle whose tangent is 1/√3, and that angle is indeed 30 degrees. This discrepancy is because the functions are inverse operations of each other; the tangent function gives the ratio given an angle, while the inverse function gives the angle given a ratio.