Understanding Arctan: Solving for 0 and 1/0

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In summary, arctan(0) is equal to 0 and not pi because of the definition of the arctan function. When using a calculator, tan(0) is equal to 0 and not pi, leading to the result of arctan(0) being 0. Similarly, arctan(1/0) is undefined but has a limit of pi/2. This is due to the definition and graph of the arctan function.
  • #1
hotmail590
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What is arctan(0)?!

I tired using my calculator (its a ti-83 plus) I hit [sec] button then [tan] then [ 0 ] and [ ) ] and it gives me 0 as answer It is in rad mode too (deg mode is same results)

I tried using the google calculator and it gives me 0 also!
http://www.google.com/search?hl=en&q=arctan(0)

BUT my math book says its pie!


Then it tried tan(pi) and indeed that does = 0!

WHY!??!? doenst arctan(0) = pi?



Another question
What is arctan(1/0) ? doens that = impossible?? (if i use my calc it says can't divide by 0)

However the answer is pi/2?!??! WHYYY


Thanks for the help
 
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  • #2
Arctan(x) = Pi means x = tan(pi)

[tex] tan(\pi) = \frac{0up}{1left} = 0 [/tex]

Arctan(x) = 0 means x = tan(0)

[tex] tan(0) = \frac{0up}{1right} = 0 [/tex]

Get it?

2. The answer is in limits.

[tex] arctan(1/0) = undefined [/tex]

However the limit is defined:

[tex] \lim x\rightarrow 0 \mbox{ of } arctan(1/x) = \frac{\pi}{2} [/tex]

Try graphing the function arctan(x) and use the trace tool to see the values at those points.
 
  • #3
Try translating [itex] tan(x) = \frac{sinx}{cosx} [/itex], you might see it more clearly.
 
  • #4
tan (2pi) = 0 too. So why doesn't arctan(0) = 2pi?

Because there's an important part of the definition of arctan that you're forgetting -- go look at it again.
 
  • #5
HINT:arctan is a function.

Daniel.
 

1. What is the value of arctan(0)?

The value of arctan(0) is 0 radians or 0 degrees.

2. How do you calculate arctan(0)?

To calculate arctan(0), use a scientific calculator or a trigonometric table to find the inverse tangent of 0, which is 0 radians or 0 degrees.

3. Why is the value of arctan(0) important in mathematics?

The value of arctan(0) is important in mathematics because it is the starting point for calculating the inverse tangent of any number. It is also used in various mathematical equations and proofs.

4. Is arctan(0) equal to 0 or undefined?

Arctan(0) is equal to 0 radians or 0 degrees, so it is not undefined. However, it is important to note that arctan(x) is undefined when x is equal to infinity or negative infinity.

5. What is the difference between arctan(0) and tan(0)?

The difference between arctan(0) and tan(0) is that arctan(0) is the inverse function of tangent, while tan(0) is the tangent function itself. Arctan(0) gives the angle whose tangent is 0, while tan(0) gives the tangent of the angle 0.

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