Proof of the tangent and cotangent identitiesProof of the Pythagorean identitiesThe proof of each of those follows from the definitions of the trigonometric functions, Topic 15.Proof of the reciprocal relationsBy definition:sin θ = yr , csc θ = ry . Therefore, sin θ is the reciprocal of ...
Journal of Mathematical Analysis & ApplicationsS. Abo Touk, Z. Al Houchan and M. El Bachraoui, Proofs for two q-trigonometric identities of Gosper. J. Math. Anal. Appl. 456(1) (2017), 662-670.S. Abo Touk, Z. Al Houchan, and M. El Bachraoui, Proofs for two q-trigonometric ...
Approximate the bounds of harmonic numbers using induction: prove by induction sum 1/k from k=1 to 2^n >= 1 + n/2 for n>=0 More examples Trigonometric Identities See the steps toward proving a trigonometric identity: does sin(θ)^2 + cos(θ)^2 = 1? Prove equalitie...
Ch 12. Rate of Change Ch 13. Rational Functions & Difference... Ch 14. Rational Expressions and Function... Ch 15. Exponential Functions & Logarithmic... Ch 16. Using Trigonometric Functions Ch 17. Trigonometric Graphs Ch 18. Trigonometric Applications Ch 19. Solving Trigonometric Identities Ch...
分类:教育 最后更新:2025-05-26 发布日期:2021-01-08 当前版本:1.0.1 成人评级:4+ 文件大小:26046464 bytes 开发人员:H3 Apps, LLC 系统平台: Mac / iPad / iPhone / 所有苹果系统 兼容性: 需要iOS12.0 或更新. 官方下载 描述 This app has 42 Trigonometric Proofs of Identities. Work on your own ...
描述 This app has 42 Trigonometric Proofs of Identities. Work on your own and then compare your answers to the steps shown in the app for proving the identity. Each step in the app is initially hidden and can be shown by clicking on the + button. 截图 ...
They are sine, cosine, tangent, cosecant, secant, and cotangent. All these trigonometric ratios are defined using thesides of the right triangle, such as an adjacent side, opposite side, and hypotenuse side. All the fundamental trigonometric identities are derived from the six trigonometric ratios...
Applying an addition formula of Liu(2007),we deduce certain Jacobi theta function identities.From these results we confirm several q-trigonometric identities conjectured by Gosper(2001).Another conjectured identity on the constant Πq is also settled.Bing HeHongcun Zhai中国科学:数学(英文版)...
q-Trigonometric functionIn 2001 W. Gosper introduced constant Πq, and conjectured many intriguing identities on this constant. In this paper we employ some knowledge of modular equations with degree 5 to confirm several of Gosper's Πq-identities. Two strange q-identities involving Πq and a ...
Proofs for certain $\\boldsymbol~q$-trigonometric identities of GosperJacobi theta functionaddition formulaq-trigonometric identityconstant Πq<正>doi:10.1007/s11425-019-9555-1BingSchoolHe,HongcunSchoolZhaiSchoolScience China(Mathematics)