How do you find the domain and range of $y=-3sin(1/2)x$ ?

Question

4079 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-02T06:42:15

Domain: all reals x
Range: $-3 <= y <= 3$

$y=-3sin(x/2)$
The amplitude is 3
The period (T) = $(2pi)/n = (2pi)/(1/2) = 4pi$

Now you can graph the equation like below.

graph{-3sin(x/2) [-10, 10, -5, 5]}

You will notice then that:
Domain: all reals x
Range: $-3 <= y <= 3$

For the range, a tip is that for the range of the sine or cosine function, the range is always between the positive and negative amplitude.

How do you find the domain and range of y=-3sin(1/2)xy=-3sin(1/2)x?