Question
Determine whether the statement is possible or impossible. \[ \sin \theta=4 \] The statement is impossible because the range of \( \sin \theta \) is (Type your answer in interval notation.)
Ask by Smith Frank. in the United States
Feb 03,2025
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Answer
The statement is impossible because the sine of an angle ranges between -1 and 1.
Solution
The statement is impossible because the range of \( \sin \theta \) is \([-1, 1]\).
\[\boxed{[-1,\ 1]}\]
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The statement is impossible because the range of \( \sin \theta \) is \([-1, 1]\). This means that the sine of any angle \( \theta \) can only take values within this interval. Since 4 is outside this range, there are no angles for which the sine equals 4.
