Solving for sin & cos of -1 ∞: Answers & Explanation

[intenzxboi]

this isn't homework 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?

 

[Mark44]

Looks like LaTeX isn't working again.

this isn't homework 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.

 

[intenzxboi]

o ok thanks so only tan-1 (x) as x goes to infinty is pi/2

 

[matt grime]

That is the simplest way to think of it. Using the symbol $\infty$ 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.