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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Updated on: 10-Oct-2022

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