### Problem StatementEvaluate the function \( f(x) = 7 \sin x - \cos \left(\frac{1}{2} x\right) \) at \( x = \frac{\pi}{3} \).### Explanation- **Function Definition**: The function \( f(x) \) is composed of two trigonometric components: \( 7 \sin x \) and \( -\cos \left(\frac{1}{2} x\right) \). - \( 7 \sin x \): This part multiplies the sine of \( x \) by 7. - \( -\cos \left(\frac{1}{2} x\right) \): This part finds the cosine of half of \( x \), then negates it.- **Evaluation Point**: We need to evaluate this function specifically at \( x = \frac{\pi}{3} \).### Steps to Solution1. **Substitute** \( x = \frac{\pi}{3} \) into the equation: \[ f\left(\frac{\pi}{3}\right) = 7 \sin\left(\frac{\pi}{3}\right) - \cos\left(\frac{1}{2} \cdot \frac{\pi}{3}\right) \]2. **Calculate Trigonometric Values**: - \(\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\) - \(\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}\)3. **Substitute the Trigonometric Values**: \[ f\left(\frac{\pi}{3}\right) = 7 \left(\frac{\sqrt{3}}{2}\right) - \frac{\sqrt{3}}{2} \]4. **Simplify**: \[ f\left(\frac{\pi}{3}\right) = \frac{7\sqrt{3}}{2} - \frac{\sqrt{3}}{2} \] \[ f\left(\frac{\pi}{3}\right) = \frac{6\sqrt{3}}{2} \] \[ f\left(\frac{\pi}{3}\right) = 3\sqrt{3} \

Name: ### Problem StatementEvaluate the function \( f(x) = 7 \sin x - \cos
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: ### Problem StatementEvaluate the function \( f(x) = 7 \sin x - \cos \left(\frac{1}{2} x\right) \) at \( x = \frac{\pi}{3} \).### Explanation- **Function Definition**: The function \( f(x) \) is composed of two trigonometric components: \( 7 \sin x