Inverse Tan Function Range: (-pi/2, pi/2)

In summary, The original range of inverse tan is (-pi/2, pi/2), and the range of tan-1(2x) is still (-pi/2, pi/2) because the domain is affected by 2x, not the range. As x goes to negative infinity, 2x goes to negative infinity and tan-1(2x) goes to -pi/2. As x goes to infinity, 2x goes to infinity and tan-1(2x) goes to pi/2.
  • #1
missmerisha
22
0

Homework Statement



State the range

y=inverse tan( 2x)

The Attempt at a Solution



The original range of inverse tan is ( -pi/2, pi/2)

Should tan inverse (2x) have (-pi, pi) as its range?
 
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  • #2
No. 2x changes x values, the domain, not the range. The range of tan-1(x) is (-pi/2, pi/2) because as x goes to negative infinity, tan-1[/sup](x) goes to -pi/2 and as x goes to infinity, tan-1(x) goes to pi/2.

As x goes to -infinity, what does 2x go to? What does tan-1
(2x) go to?
As x goes to infinity, what does 2x go to? What does tan-1
(2x) go to?
 

What is the inverse tangent function?

The inverse tangent function, denoted as arctan(x) or tan-1(x), is the inverse of the tangent function. It calculates the angle whose tangent is equal to a given number.

What is the range of the inverse tangent function?

The inverse tangent function has a range of (-π/2, π/2). This means that the output of the function will always be between -π/2 and π/2, inclusive.

What is the domain of the inverse tangent function?

The domain of the inverse tangent function is all real numbers, except for ±π/2. This is because the tangent function is undefined at these values.

What is the relationship between the inverse tangent function and the tangent function?

The inverse tangent function is the inverse of the tangent function. This means that if we input the output of the tangent function into the inverse tangent function, we will get back the original value.

What are some practical applications of the inverse tangent function?

The inverse tangent function is commonly used in mathematics, physics, and engineering to calculate angles and solve trigonometric equations. It is also used in computer graphics to determine the direction of an object's movement based on its coordinates.

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