Question

Range of the function f(x)=tan-1x is​

Answer 1

Answer:

Here we a have a right triangle where we know the lengths of the two legs, that is, the sides opposite and adjacent to the angle. So, we use the inverse tangent function. If you enter this into a calculator set to "degree" mode, you get

tan − 1 ( 10 3 ) ≈ 73.3 °

If you have the calculator set to radian mode, you get

tan − 1 ( 10 3 ) ≈ 1.28

If you've committed to memory the side length ratios that occur in 45 − 45 − 90 and 30 − 60 − 90 triangles, you can probably find some values of inverse trigonometric functions without using a calculator.

Example 2:

Find cos − 1 ( 3 2 ) .

You may recall that in a 30 − 60 − 90 triangle, if the hypotenuse has length 1 , then the long leg has length 3 2 . Since cosine is the ratio of the adjacent side to the hypotenuse, the value of the inverse cosine is 30 ° , or about 0.52 radians.

cos − 1 ( 3 2 ) = 30 °

Graphs of Inverse Trigonometric Functions

Trigonometric functions are all periodic functions .  Thus the graphs of none of them pass the Horizontal Line Test and so are not 1 − to − 1 .  This means none of them have an inverse unless the domain of each is restricted to make each of them 1 − to − 1 .

Since the graphs are periodic, if we pick an appropriate domain we can use all values of the range .

If we restrict the domain of f ( x ) = sin ( x ) to [ − π 2 , π 2 ] we have made the function 1 − to − 1 .  The range is [ − 1 , 1 ] .

Answer 2

Answer:

the range of f(X)=tan-1x is (-1,1)

Step-by-step explanation:

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