Question
Let $f(x)=\sin x$(a) Find $f(\pi / 6)$(b) Use a graph to estimate an interval $(a, b)$ about $x=\pi / 6$ so that $0.3<f(x)<0.7$ provided $a<x<b$(c) Use a graph to estimate an interval $(a, b)$ about $x=\pi / 6$ so that $0.49<f(x)<0.51$ provided $a<x<b$
Step 1
We know that $f(x) = \sin x$, so we substitute $\pi / 6$ into the function: \[f(\pi / 6) = \sin (\pi / 6)\] Using the unit circle or a calculator, we find that $\sin (\pi / 6) = 1/2$. So, $f(\pi / 6) = 1/2$. Show more…
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