Question

State whether the following statements are true or false. Justify your answer.

$\sin \theta =\frac{4}{3}$ for some angle $\theta$.

• A. True
• B. False

Answer 1

The correct option is B False

Sine:

The sine of an angle can be defined as the ratio of the length of the perpendicular to the length of the hypotenuse in a right-angled triangle.The domain of sine function is all real numbers as sin x is defined for all x in (-∞, ∞). Whereas the range of sin x is [-1, 1] as the value of sin x does not go beyond this.

The maximum value of the $\sin \theta$ is equal to $1$.

$$\begin{gathered} \sin \theta =\frac{4}{3} \\ =1.34 \end{gathered}$$

The value of $\sin \theta$ can not be greater than $1$.

Hence, the given statement is false.