Traditional chaotic maps struggle with narrow chaotic ranges and inefficiencies, limiting their use for lightweight, secure image encryption in resource-constrained Wireless Sensor Networks (WSNs). We propose the SPCM, a novel one-dimensional discontinuous chaotic system integrating polynomial and sine functions, leveraging a piecewise function to achieve a broad chaotic range ( $r\in [0,12]$) and a high Lyapunov exponent (5.04). Validated through nine benchmarks, including standard randomness tests, Diehard tests, and Shannon entropy (3.883), SPCM demonstrates superior randomness and high sensitivity to initial conditions. Applied to image encryption, SPCM achieves 0.152582 s (39% faster than some techniques) and 433.42 KB/s throughput (134% higher than some techniques), setting new benchmarks for chaotic map-based methods in WSNs. Chaos-based permutation and exclusive or (XOR) diffusion yield near-zero correlation in encrypted images, ensuring strong resistance to Statistical Attacks (SA) and accurate recovery. SPCM also exhibits a strong avalanche effect ( $>50\mathrm{\%}$ bit difference), making it an efficient, secure solution for WSNs in domains like healthcare and smart cities.