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

[so_gr_lo]

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 ?

 

[anuttarasammyak]

2sin x has period $2\pi$ so both the minimum and the maximum value are realized in the domain. Draw the graph.

 

[FactChecker]

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.

 

[so_gr_lo]

yeah I think that might be what is expected, thanks