What is the domain of a trig function with y = 2sin(x)?

In summary, the function y = 2sin(x) has a period of 2π and a domain of -π < x ≤ π. The minimum and maximum values of the function are -2 and 2, respectively, which are both within the domain. Using the continuity of the function, it can be concluded that all values between -2 and 2 are also covered by the function. Graphing the function can also visually show this behavior. It is recommended to find the values of x that output -2 and 2 and demonstrate that they are within the domain.
  • #1
so_gr_lo
69
10
Homework Statement
I am supposed to find the limits of a trig function, which I have managed to do, but I don’t know how to show that the range can be achieved within the given domain.
Relevant Equations
y = 2sin(x)
y = 2sin(x)

-1≤ sin(x) ≤ 1

-2 ≤ 2sin(x) ≤ 2

so -2 and 2 are the max/min limits

but the domain is -π < x ≤ π

Do I find the values of x that outputs -2 and 2 and show that they are within the domain ?
 
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  • #2
2sin x has period ##2\pi## so both the minimum and the maximum value are realized in the domain. Draw the graph.
 
  • #3
so_gr_lo said:
Do I find the values of x that outputs -2 and 2 and show that they are within the domain ?
That is a good approach. Then use the continuity of the function to say that it covers everything in between.
 
  • #4
yeah I think that might be what is expected, thanks
 

Related to What is the domain of a trig function with y = 2sin(x)?

What is the domain of a trig function?

The domain of a trigonometric function is the set of all possible input values for which the function is defined. In other words, it is the set of all values for the independent variable that produce a valid output for the function.

How do you determine the domain of a trig function?

To determine the domain of a trigonometric function, you need to consider any restrictions on the input values. For example, if the function contains a square root, the input values must be non-negative. Additionally, trigonometric functions have a periodic nature, so the domain may need to be restricted to a certain interval to avoid repeating values.

What is the domain of a sine function?

The domain of a sine function is all real numbers, as there are no restrictions on the input values. However, if the function is being used to model a real-world situation, the domain may need to be restricted to a certain interval to make sense in the context of the problem.

Can the domain of a trig function be infinite?

Yes, the domain of a trigonometric function can be infinite if there are no restrictions on the input values. However, in some cases, the domain may be limited to a finite interval to avoid repeating values or to make the function more practical in real-world applications.

What happens if the input value is outside the domain of a trig function?

If the input value is outside the domain of a trigonometric function, the function is considered undefined. This means that there is no valid output for that particular input value, and the function cannot be evaluated at that point.

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