The Two Interpretations Of Tan2X: Trigonometric Function Explained And Evaluated Using Unit Circle And Identities

tan2x

2tan/1-tan^2

The trigonometric function tan2x can be interpreted in two ways: either as tangent of 2x radians, or as the tangent of the product of the tangent of x and 2. In the first interpretation, you simply evaluate the tangent function at 2x, yielding:

tan2x = tan(2x)

In the second interpretation, you need to first find the tangent of x, and then multiply it by 2:

tan2x = tan(x) * 2

Both interpretations are useful in different contexts. The first one is often used in calculus, where trigonometric functions are frequently encountered. The second one is often used in geometry, where angles are often expressed as ratios of side lengths in right triangles.

To evaluate the function in either case, you can use a variety of techniques, including the unit circle, trigonometric identities, or the calculator. For example, if x = π/4, then:

tan2x = tan(2π/4) = tan(π/2) = undefined

Here, we used the fact that tangent is undefined at odd multiples of π/2, including π/2 itself.

More Answers: