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State whether the following are true or false. Justify your answer.
\( \sin \theta=\frac{4}{3} \) for some angle \( \theta \).
Given:
Given statement is:
\( \sin \theta=\frac{4}{3} \) for some angle \( \theta \).
To do:
We have to state whether the given statement is true or false.
Solution:
Let $\sin \theta=\sin\ A =\frac{side\ opposite\ to\ A}{Hypotenuse}$
$=\frac{BC}{AC}$
In a triangle ABC, $AC$(Hypotenuse) is greater than $BC$.
Therefore,
$\frac{BC}{AC}$ is less than 1. It is equal to 1 when angle A is equal to zero but never greater than 1.
This implies \( \sin \theta≠\frac{4}{3} \) for any value of angle \( \theta \).
The given statement is false.
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