Problem

Decide whether the statement is possible or impossible.
\[
\sin \theta=-0.5
\]
Is the statement possible or impossible?
A. The statement is impossible because the range of $\sin \theta$ is $[0, \infty)$.
B. The statement is impossible because the range of $\sin \theta$ is $(-\infty,-1] \cup[1, \infty)$.
C. The statement is possible because the range of $\sin \theta$ is $(-\infty, 0]$.
D. The statement is possible because the range of $\sin \theta$ is $[-1,1]$.

Answer

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Answer

Final Answer: The statement is possible because the range of \(\sin \theta\) is \([-1,1]\). So, the correct option is \(\boxed{\text{(D)}}\).

Steps

Step 1 :Decide whether the statement is possible or impossible.

Step 2 :The sine function, denoted by sin, is a trigonometric function of an angle. The sine of an angle is defined in the context of a right triangle: for the specified angle, the sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse).

Step 3 :The range of the sine function is the set of all possible output values (y-coordinates), which is the interval [-1,1]. Therefore, the statement \(\sin \theta=-0.5\) is possible because -0.5 is within the range of the sine function.

Step 4 :Final Answer: The statement is possible because the range of \(\sin \theta\) is \([-1,1]\). So, the correct option is \(\boxed{\text{(D)}}\).

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