Find possible values values for sin(thetha)= sin30

Question

Hi, I dont know what is meant by the question. 

Answer 1

The function y=sin(x) is a function (with one value of y for each value of x).  However, there are many values of x that produce the same value of y.  That is clear when you look at the graph of y=sin(x) [and perhaps draw a horizontal line for y to find like values].

 

The question is asking you to provide some examples of "theta" (that is, Θ in uppercase and θ in lowercase) for which:

    sin(Θ) = sin(30°)

 

Of course, Θ = 30° is one (but decide whether you want to provide such an obvious answer).

 

Now, what other values of Θ have the same value of sin(Θ) as sin(30°)?

 

 

Answer 2

sin θ = sin 30

sin θ = 0.5

θ ∈ {30 + 360k} ∪ {120 + 360k} where k ∈ Z