Question

How do I determine the domain for the following sinusoidal functions?

a.) j(x)=0.5sin(2x-30)
b. 10sin(180(t-17))-30

Answer 1

@mathstudent55

Answer 2

@satellite73

Answer 3

@3mar

Answer 4

Well, I am here.

**I am sorry for late!
The electricity was off!

\(\color{MediumOrchid }{Domain}\) is the set of points\values that related to the independent variable (x) which make the function defined!

For our case, there is no limit or restriction of x to be any value (from \(-\infty\) to \(+\infty~\)) so the domain would be all the real numbers \(\color{BlueViolet }R~\).

Answer 5

SO that is applies on both functions you have provided above!

Test them also at this graph and search for the points\values of the domain that make the function(s) is not defined!. [you will never find any.... ;) ]

a.) j(x)=0.5sin(2x-30)
https://www.desmos.com/calculator/sgwyikefqg

b.) f(t)=10sin(180(t-17))-30
https://www.desmos.com/calculator/q3tnrjfzcp

*hint:
the range of both sine and cosine functions [-a,a], where a is the amplitude of the function.