State whether the following statement is True or False and justify your answer: "The value of sin A can be gr…

Question

State whether the following statement is True or False and justify your answer: "The value of sin A can be greater than 1 for some acute angle A."

Accepted Answer

## Model Answer **False.** By definition, $\sin A = \dfrac{	ext{side opposite to angle A}}{	ext{hypotenuse}}$. Since the hypotenuse is the longest side of a right triangle, the side opposite to angle A is always less than or equal to the hypotenuse. Therefore, $\sin A \leq 1$ for any acute angle A. Its value can never exceed 1. *Source: Chapter 8 – Introduction to Trigonometry, Section 8.2 (Remark) and Section 8.5 (Summary point 5)* --- ## Explanation - Examiners expect: (1) the word **False**, (2) a reason using the definition of sin A as a ratio of two sides of a right triangle, (3) the key fact that hypotenuse is the longest side. - Summary point 5 explicitly states: *"The value of sin A or cos A never exceeds 1."* - Don't just state False — the justification carries the marks (likely 1 mark for statement + 1 mark for reason).

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