Need help with determing domains of sin, cos, and tan

In summary, the domain for sin and cos is (-inf , + inf) and for tan it is All real numbers except pi/1 + n*Pi but for csc it is All real numbers except n*Pi
  • #1
name_ask17
146
0

Homework Statement



Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses.

i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)
and then for tan it is All real numbers
except pi/1 + n*Pi
but then for csc, it is All real numbers
except n*Pi

Can you explain why? I think I'm having trouble with figuring out how to find domains and I want to understand this before I start calculus. Please explain.
 
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  • #2
You might want to check the expression for x where tan x goes to +inf or -inf.
 
  • #3
You need to try a little yourself before asking, but I'll aid you this once..

Tan(x) = Sin(x)/Cos(x)

csc(x) = 1/Sin(x)

What's the rule for dividing?
 
  • #4
name_ask17 said:

Homework Statement



Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses.

i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)
and then for tan it is All real numbers
except pi/1 + n*Pi
I don't know what to make of "pi/1 + n*Pi ". The domain for the tangent function is all real numbers x, such that x ≠ (2n + 1)∏/2, where n is an integer. IOW, all reals except odd multiples of ∏/2.
 
  • #5
name_ask17 said:
and then for tan it is All real numbers
except pi/1 + n*Pi
Correction: this should be
[tex]\frac{\pi}{2} + n\pi[/tex]
. And you have to specify what n can equal, as Mark44 said.
 
  • #6
Hi Name_Ask,

I'd like you to go to http://www.touchtrigonometry.org/" and play around with it a little bit.

While you're there, make sure to do the following:

  • Look at the bottom left of the screen where you see the tig. function names and a value beside each.
  • Turn them all off by clicking on them.
  • Turn one on at a time.
  • Take notice of how often its pattern repeats, and when it starts.
  • Examine all the "x" values it can hold and the ones that are impossible.
  • Why are some of these Tig values impossible?
  • Click the active graph at any time to "Pause" your mouse, and look at what the line does on the Trig Circle to the left.
  • Compare what you see with your knowledge of what happens when a number is divided by 0.
  • Repeat with a new trig function.
 
Last edited by a moderator:

1. What is the definition of a domain?

A domain is the set of all possible input values for a function. In other words, it is the set of numbers that can be plugged into the function to produce a valid output.

2. How do I determine the domain of a trigonometric function?

The domain of a trigonometric function, such as sin, cos, or tan, is all real numbers. This means that any value can be plugged into the function and it will produce a valid output. However, there may be restrictions on the domain for certain types of problems, such as when using inverse trigonometric functions.

3. Can the domain of a trigonometric function be negative?

Yes, the domain of a trigonometric function can include negative values. For example, the domain of sin(x) is all real numbers, including negative values. However, when dealing with inverse trigonometric functions, the domain may be restricted to only positive or non-negative values.

4. How do I find the domain of a composite trigonometric function?

To find the domain of a composite trigonometric function, you need to consider the domains of each individual function within the composite. The overall domain will be the intersection of the individual domains. This means that the input values must be valid for all functions within the composite in order to produce a valid output.

5. Are there any common mistakes to avoid when determining the domain of a trigonometric function?

One common mistake when determining the domain of a trigonometric function is forgetting to consider any restrictions on the domain, such as when using inverse trigonometric functions. Another mistake is not accounting for any restrictions on the input values, such as when using a calculator that only accepts values within a certain range. It is important to carefully consider all possible restrictions when determining the domain of a trigonometric function.

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