1. **State the problem:** We need to determine the length of the period of a sinusoidal function that oscillates between 5 and -5. 2. **Given information:** The function peaks at approximately 75° and again at 225°. 3. **Recall the period of a sinusoidal function:** The period is the horizontal length over which the function completes one full cycle and repeats. 4. **Calculate the period:** The distance between two consecutive peaks is the period. 5. **Find the difference between the peaks:** $$225^\circ - 75^\circ = 150^\circ$$ 6. **Interpretation:** The period is 150°, but the choices given are 90° and 300°. 7. **Check if the function is a sine or cosine:** For sine and cosine, the distance between two peaks is the period. 8. **Since 150° is not an option, consider the full cycle:** The function might have a period of 300° because the distance between two peaks is half the period (for sine and cosine, peaks are half a period apart). 9. **Conclusion:** The period is $$300^\circ$$. **Final answer:** The length of the period is 300°.