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Chapter 6: Q 121 (page 397)

Show that the range of the tangent function is the set of all real numbers

Short Answer

Expert verified

As tangent function takes values from -鈭�to鈭�, we can conclude that the range of tangent function is set of all real values.

Step by step solution

01

Step 1. Given Information

We have to show that the range of a tangent function is set of all real numbers.

02

Step 2. Explanation

We know that a tangent function y=tanxis a periodic function of period 蟺. Also it continuous from -蟺2to蟺2.

The value of tan蟺2=鈭�and the value of tan-蟺2=-鈭�. Also tan0=0.

From these valuers we can see that the tan functions takes values from -鈭�to 鈭�.

So we can conclude that the range of tangent function is set of all real values.

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