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Tan -1 of infinity

  • Thread starter intenzxboi
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  • #1
98
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this isn't hw just wanted to know what the values are.

tan -1 (infinity) = pi/2
tan-1 (0) = 0

what is sin -1 infinty and cos -1 infinity?
 

Answers and Replies

  • #2
33,171
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Looks like LaTeX isn't working again.

this isn't hw just wanted to know what the values are.

tan -1 (infinity) = pi/2
tan-1 (0) = 0
The second one is correct, but not the first one. What you can say, though, is that
lim(x -->infinity) tan-1(x) = pi/2

The domain of the inverse tangent function is all real numbers, but neither -infinity nor infinity is included in that set.
what is sin -1 infinty and cos -1 infinity?
The domain for sin-1(x) is usually taken as [-pi/2, pi/2], and the domain for cos-1(x) is usually taken as [0, pi]. These intervals are chosen to make these function one-to-one, which a function has to be in order for it to have an inverse.

Unline tan-1(x), neither the inverse sine nor inverse cosine have limits as x approaches infinity, so the answer to your last questions is that they aren't anything.
 
  • #3
98
0
o ok thanks so only tan-1 (x) as x goes to infinty is pi/2
 
  • #4
matt grime
Science Advisor
Homework Helper
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That is the simplest way to think of it. Using the symbol [itex]\infty[/itex] is often useful shorthand for the same thing. It can also be put on a sound rigorous footing geometrically (projective space) or analytically (Riemann sphere), but that requires using spaces strictly larger than the real (or complex) numbers.
 

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