How do you find the domain and range of $g(t) = 3 sin t$ ?

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Answer 1 · 2018-07-11T11:58:25

Domain: $t\in\mathbb R$ & range: $[-3, 3]$

Given function:

$g(t)=3\sin t$

The above trigonometric function $g(t)=3\sin t$ is continuous every where so its domain is the entire set of real numbers i.e. $t\in \mathbbR$

We know that

$-1\le\sin t\le1$

$-3\le 3\sin t\le 3$

hence, the range of given function is $[-3, 3]$

How do you find the domain and range of g(t) = 3 sin tg(t) = 3 sin t?