Fungsi Simetri pada Koordinat Kutub dan Karakteristiknya
Keywords:
Fungsi ganjil, fungsi genap, fungsi simetri, koordinat kutubAbstract
Pada sistem koordinat kutub, grafik fungsi ganjil simetri terhadap garis ???? = ????/2, tetapi tidak berlaku sebaliknya, yakni jika suatu fungsi grafiknya simetri terhadap garis ???? = ????/2 tidak perlu merupakan fungsi ganjil. Grafik fungsi genap simetri terhadap sumbu kutub (garis ???? =0), tetapi tidak berlaku sebaliknya, yakni jika suatu fungsi grafiknya simetri terhadap sumbu kutub tidak perlu merupakan fungsi genap. Tujuan penelitian ini adalah mengenalkan fungsi simetri terhadap garis tertentu pada sistem koordinat kutub dengan metode menggeneralisasi fungsi ganjil atau fungsi genap. Selain itu, beberapa karakteristik fungsi simetri pada sistem koordinat kutub akan dibahas dan hasilnya dituangkan dalam teorema-teorema. Hasil yang diperoleh bahwa fungsi simetri terhadap garis grafiknya simetri terhadap garis namun suatu fungsi yang grafiknya simetri terhadap garis belum menjamin merupakan fungsi simetri terhadap garis Hasil lain yang diperoleh adalah kombinasi linear fungsi-fungsi simetri merupakan fungsi simetri.
Downloads
References
Borji, V., & Voskoglou, M. (2016). Applying the APOS theory to study the student understanding of polar coordinates. American Journal of Educational Research, 4(16), 1149–1156. https://doi.org/10.12691/education-4-16-5
Daniel, J., Ayinde, K., Dudu, E. E., & Eberechukwu, O. I. (2024). Application of polar coordinates in the summation of the Gaussian distribution. RT&A, 19(2), 408–424.
Gamero-Castillero, J. A., Quiñones-Rodríguez, Y., Apollaro, G., Hernández-Mendo, A., Morales-Sánchez, V., & Falcó, C. (2022). Application of the polar coordinate technique in the study of technical-tactical scoring actions in taekwondo. Frontiers in Sports and Active Living, 4, Article 877502. https://doi.org/10.3389/fspor.2022.877502
Haro, A., & Aguilar, M. S. (2024). Learning obstacles and teaching proposals associated with the polar coordinate system: A literature review. International Journal of Experimental Mathematics and Science Technology, 56(5), 828–850. https://doi.org/10.1080/0020739X.2023.2295903
Hass, J., Heil, C., & Weir, M. (2018). Thomas’ calculus (14th ed.). Pearson.
Herman, E., & Strang, G. (2020). Calculus, volume I. OpenStax, Rice University.
Kumar. (2023). An overview on polar plots r = 1 + 2m cos(θ). IOSR Journal of Mathematics, 19(5), 59–69. https://doi.org/10.9790/5728-1905025969
Lee, G., & Kim, W. (2024). Image processing in L1-norm-based discrete Cartesian and polar coordinates. Electronics, 13(6), 1–12.
Lippman, D., & Rasmussen, M. (2018). Precalculus: An investigation of functions (Version 2.1). Creative Commons.
Marzuki, M., Sudiarta, I. W., Ardianto, T., Illahi, R. R., Wijaya, N. I., & Ariani, T. O. (2023). Pengenalan sistem koordinat polar dalam pembahasan materi gerak melingkar bagi siswa MAN 1 Lombok Timur. Jurnal Pepadu, 4(3), 435–440. https://doi.org/10.29303/pepadu.v4i3.3605
Nauryzbayeva, R. M. (2020). An oblique asymptote of functions in polar coordinate system. Journal of Advances in Mathematics and Computer Science, 4(1), 1–4. https://doi.org/10.26855/jamc.2020.03.001
Rahmani-Andebili, M. (2021). Calculus: Practice problems, methods, and solutions. Springer Nature.
Schlicker, S., Keller, M. T., & Long, N. (2024). Active calculus: Multivariable. Creative Commons.
Shatnawi, M., Nasrudin, M. F., & Sahran, S. (2017). A new initialization technique in polar coordinates for particle swarm optimization and polar PSO. International Journal of Applied Engineering Science and Information Technology, 7(1), 242–249.
Simón, P. D., D’Ascoli, S., Chemla, E., Lakretz, Y., & King, J. R. (2024). A polar coordinate system represents syntax in large language models. In Proceedings of the 38th Conference on Neural Information Processing Systems. https://doi.org/10.48550/arXiv.2412.05571
Strang, G. (2016). Calculus, volume II. OpenStax.
Volkova, S. N., Shleenko, A. V., & Sivak, E. E. (2020). Algorithm for designing building constructions expressed by nonlinear functions. IOP Conference Series: Materials Science and Engineering, 911, Article 012011. https://doi.org/10.1088/1757-899X/911/1/012011
Zhang, S. W., Wang, J. S., Li, Y. X., Zhang, S. H., Wang, Y. C., & Wang, X. T. (2024). Improved honey badger algorithm based on elementary function density factors and mathematical spirals in polar coordinate systems. Artificial Intelligence Review, 57, Article 55. https://doi.org/10.1007/s10462-023-10658-2
Zhou, L., Wei, H., Li, H., Zhao, W., Zhang, Y., & Zhang, Y. (2020). Object detection for remote sensing images based on polar coordinates. IEEE Access, 8, 223373–223384.
Zhu, J., Wang, Y., Gao, F., & Zhang, Z. (2023). Optical differentiation in a polar coordinate system. Applied Physics Letters, 122(9). https://doi.org/10.1063/5.0140272
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Firdaus Ubaidillah, Kosala Dwidja Purnomo, Bagus Julianto
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
