F(x)=cos(x-p/3)

The given function is \( f(x) = \cos(x - \frac{\pi}{3}) \). This is a cosine function that has been horizontally shifted. ### Key Properties of the Function: 1. **Period**: The period of the cosine function is \( 2\pi \). Thus, the period of \( f(x) \) is also \( 2\pi \). 2. **Amplitude**: The amplitude of \( \cos(x) \) is 1. No vertical scaling is applied here, so the amplitude of \( f(x) \) is also 1. 3. **Phase Shift**: The expression \( x - \frac{\pi}{3} \) indicates a phase shift to the right by \( \frac{\pi}{3} \). 4. **Vertical Shift**: There is no vertical shift in this case as there is no constant added to the cosine function. ### Important Points: - The cosine function starts at its maximum value. Since there is no vertical shift, the maximum value of \( f(x) \) is \( 1 \), occurring at \( x = \frac{\pi}{3} + 2k\pi \) (where \( k \) is any integer). - The minimum value of \( f(x) \) is \( -1 \), occurring at \( x = \frac{\pi}{3} + (2k + 1)\pi \). ### Summary: - **Function**: \( f(x) = \cos(x - \frac{\pi}{3}) \) - **Period**: \( 2\pi \) - **Amplitude**: 1 - **Phase Shift**: Right by \( \frac{\pi}{3} \) - **Max Value**: 1 at \( x = \frac{\pi}{3} + 2k\pi \) - **Min Value**: -1 at \( x = \frac{\pi}{3} + (2k + 1)\pi \) If you need to analyze or visualize the graph of this function, let me know!