Questions: Let f(x)=sin x and h(x)=2 x. Find the value of (f ∘ h)(π/6).

Solution Steps

To solve for \((f \circ h)\left(\frac{\pi}{6}\right)\), we need to first find \(h\left(\frac{\pi}{6}\right)\) and then apply the function \(f\) to the result. Specifically, we will:

1. Compute \(h\left(\frac{\pi}{6}\right) = 2 \cdot \frac{\pi}{6}\).
2. Use the result from step 1 as the input to \(f(x) = \sin x\).

First, we need to evaluate the function \( h(x) = 2x \) at \( x = \frac{\pi}{6} \): \[ h\left(\frac{\pi}{6}\right) = 2 \cdot \frac{\pi}{6} = \frac{\pi}{3} \]

Next, we use the result from Step 1 as the input to the function \( f(x) = \sin x \): \[ f\left(h\left(\frac{\pi}{6}\right)\right) = f\left(\frac{\pi}{3}\right) = \sin\left(\frac{\pi}{3}\right) \]

We know that: \[ \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \approx 0.8660 \]

Final Answer