Find the Range y=tan(x)

Problem

y=tan(x)

Solution

1. Identify the definition of the function y=tan(x) in terms of sine and cosine.

y=sin(x)/cos(x)

2. Analyze the behavior of the function as x approaches the vertical asymptotes, which occur where cos(x)=0

x=π/2+n*π

3. Observe the limits of the function as x approaches these asymptotes from the left and the right.

(lim_x→π/2−)(tan(x))=∞

(lim_x→π/2+)(tan(x))=−∞

4. Determine the set of all possible output values based on the fact that the function is continuous on the interval (−π/2,π/2) and spans from negative infinity to positive infinity.

Range=(−∞,∞)

Final Answer

Range of *y=tan(x)* is *(−∞,∞)

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