State the value of $$ \lim_{h \to 0} \frac{\sin(\pi + h) - \sin \pi}{h} $$ Circle your answer - AQA - A-Level Maths Pure - Question 2 - 2022 - Paper 2

To evaluate the limit, we can use the property of the sine function. We know that:

$\sin(\pi + h) = -\sin(h)$

Thus, the expression becomes:

$\lim_{h \to 0} \frac{-\sin(h) - 0}{h} = -\lim_{h \to 0} \frac{\sin(h)}{h}$

Using the standard limit result that $\lim_{h \to 0} \frac{\sin(h)}{h} = 1$, we have:

$-\lim_{h \to 0} \frac{\sin(h)}{h} = -1$

Therefore, the value is -1.