# Trigonometry | Krishna Series

Contents

This book Trigonometry has been specially written according to the latest Unified Syllabus to meet the requirements of the B.A. and B.Sc. Part-I Students of all Universities in Uttar Pradesh.

This book is important for UPSC Optional, IIT JEE Mains, Graduation College Students BSC all sem (1st, 2nd, 3rd year), BA (1st, 2nd, 3rd, 4th, 5th, 6th semester), Engineering, Preparing for SSC, Banking And Other Competitive Examination.

### Syllabus

Algebra

Unit-1: Sequence and its convergence (basic idea), Convergence of infinite series, Comparison test, ratio test, root test, Raabe’s test, Logarithmic ratio test, Cauchy’s condensation test, DeMorgan and Bertrand test and higher logarithmic ratio test. Alternating series, Leibnitz test, Absolute and conditional convergence, Congruence modulo m relation, Equivalence relations, and partitions.

Unit-2: Definition of a group with examples and simple properties, Permutation groups, Subgroups, Centre and normalizer, Cyclic groups, Coset decomposition, Lagrange’s theorem, and its consequences.

Unit-3: Homomorphism and Isomorphism. Cayley’s theorem, Normal subgroups, Quotient group, Fundamental theorem of homomorphism, Conjugacy irelation, Class equation, Direct product.

Unit-4: Introduction to rings, subrings, integral domains, and fields, characteristics of a ring, Homomorphism of rings, Ideals, and Quotient rings.

Trigonometry

Unit-5: Complex functions and separation into real and imaginary parts, Exponential, Direct and inverse trigonometric and hyperbolic functions, Logarithmic functions, Gregory’s series, Summation of series.