How to find the domain of the sine - ACT Math

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Question

Find the domain of the function: $y=-9\sin(5\theta-3)-3$

Answer

The function $y=-9\sin(5\theta-3)-3$ is related to the parent function $y=\sin(\theta)$ , which has a domain of $(-\infty.\infty)$ .

The value of theta for $y=-9\sin(5\theta-3)-3$ has no restriction and is valid for all real numbers.

The answer is $(-\infty,\infty)$ .

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Question

What is the domain of the given trigonometric function:

$z(t) = 2\sin(-2t)$

Answer

For both Sine and Cosine, since there are no asymptotes like Tangent and Cotangent functions, the function can take in any value for . Thus the domain is:

$(-\infty,\infty)$

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