{"paper":{"title":"On certain q-trigonometric identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Bing He","submitted_at":"2019-06-25T04:35:05Z","abstract_excerpt":"Finding theta function (or $q$-)analogues for well-known trigonometric identities is an interesting topic. In this paper, we first introduce the definition of $q$-analogues for $\\mathrm{tan}z$ and $\\mathrm{cot}z$ and then apply the theory of elliptic functions to establish a theta function identity. From this identity we deduce two $q$-trigonometric identities involving $\\mathrm{tan}_{q}z$ and $\\cot_{q}z,$ which are theta function analogues for two well-known trigonometric identities concerning $\\mathrm{tan}z$ and $\\cot z.$ Some other $q$-trigonometric identities are also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00711","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}