Precalculus and Trigonometry

Name: Precalculus and Trigonometry
Rating: 5.0 (6 reviews)

A complete course on Pre calculus and Trigonometry

Created bySandeep Kumar Mathur

Last updated 7/2026

English

What you'll learn

Complex numbers:Introduction to Imaginary Numbers,vComplex Numbers,voperations ,conjugate and Modulus etc.
De-Moivre's Theorem
Rational Expressions
Partial Fractions
Composite and Inverse Functions
Arithmetic Progressions:Selection of terms in an A.P.,Sum of n terms of an A.P. etc
Geometric Progressions:Selection of Terms in G.P.,Sum of n terms of a G.P.,Sum to infinity in a G.P etc.
Harmonic Progression: Harmonic mean etc.
Combinatorics :Factorial Notations,Fundamental Principle of Counting,Permutations and Combinations
Probability
Trigonometry: Introduction to Trigonometric Ratios, Trigonometric Ratios of some Particular Angles, Trigonometric Ratios of Complementary Angles,identities etc.
Heights and Distances Pronlems
Analytical Geometry:Basic Concepts of Straight Lines,
The Circle

Course content

21 sections • 588 lectures • 48h 48m total length

Introduction to Imaginary Numbers8:03
Example-13:05
Example-21:58
Example-31:52
Example-43:13
Quiz
Complex Numbers,operations ,conjugate and Modulus39:24
Example-115:43
Example-21:58
Example-35:17
Example-43:41
Example-513:54
Example-65:40
Example-73:15
Example-88:56
Example-96:11
Example-102:46
Illustrates computing the product of a complex number and its conjugate using (3-2i)(3+2i) and the z zbar = |z|^2 property, yielding 13.
Example-112:55
Example-125:40
Example-133:54
Example-141:36
Quiz
Cube roots of Unity11:43
Example-11:39
Example-23:09
Example-33:36
the lecturer shows simplifying a fraction with omega by multiplying by omega or omega^2, using omega^3=1 and 1+omega+omega^2=0 to obtain -1, hence option B.
Example-43:19
Solve a cube root of unity problem by expressing one plus omega to the seventh as a plus b omega, and show that a and b are both one.
Example-58:39
Example-64:30
Example-76:03
Example-86:53
Example-94:05
Example-1012:02
Quiz
Representation of a Complex Number18:32
Example-18:13
Example-210:35
Learn to convert complex numbers to polar form by finding modulus and theta, then write as r cos theta plus i sine theta. Includes several examples and quadrant reasoning.
Example-32:09
Example-41:51
Example-55:04
Example-62:11
Example-75:01
Example-87:07
Quiz
Distance between two Points and Section Formula6:30
Example-14:32
Example-23:03
Example-33:51
Example-47:17
Example-56:28
Quiz
Equation of a Circle2:47
Example-14:18
Identify the circle center and radius from modulus equations, using z0 as the center and r as the radius, with examples and standard form conversion to reveal their values.
Example-24:51
Example-38:09
Example-48:14
Quiz

Basic Concepts9:07
Example-11:58
Example-21:16
Example-33:01
Apply de Moivre's theorem to simplify a complex expression by transforming into cos theta plus iota sine theta, combining powers, and canceling terms to obtain a final value of one.
Example-44:39
Example-58:45
Example-64:19
Example-711:11
Example-86:55
Example-95:06
Express root three plus i and root three minus i in polar form as 2(cos pi/6 ± i sin pi/6), then apply De Moivre to obtain 2^{n+1} cos(n pi/6).
Example-107:04
n Roots of a Complex number5:32
Example-15:43
Example-27:49
Example-37:19
nth Roots of Unity7:01
Example-11:52
Quiz

Introduction12:57
Example-16:01
Example-22:16
Example-35:14
Example-43:43
Example-54:53
Example-63:19
Example-73:00
Example-84:17
Example-93:26
Example-105:59
Quiz
Selection of terms in an A.P.3:59
Example-15:57
Quiz
Arithmetic Mean between two numbers4:19
Example-12:27
Example-22:00
Example-32:24
Sum of n terms of an A.P.7:46
Learn to find the sum of the first n terms of an arithmetic progression using s_n = n/2 (a + l) or s_n = n/2 [2a + (n-1)d].
Example-11:37
Example-23:19
Example-36:23
Example-44:19
Example-53:24
Example-63:34
Example-75:41
Example-88:41
Example-97:04
Example-103:14
Example-118:42
Quiz
Properties of A.P.13:28
Example-13:26
Example-25:02
Example-33:52
If a, b, c are in AP, 1/(√b+√c), 1/(√c+√a), and 1/(√a+√b) form an AP. The condition 2b = a + c characterizes this.
Example-41:57
Example-56:08
Example-66:14
Example-72:22
Example-84:27
Example-93:36
Example-104:15
Solve for x in a logarithmic arithmetic progression using base-ten logs and the base-change formula, yielding x = log base 2 of 5.
Example-115:47
Quiz
Insertion of AM's5:06
Example-12:15
Example-24:02
Example-35:47
Example-43:33
Example-55:22
Example-63:05
Quiz

Introduction9:23
Example-13:32
Example-25:50
Example-32:41
Example-43:50
Example-53:08
Example-63:38
Example-74:04
Example-85:59
Example-91:41
Example-107:04
Example-114:37
Example-122:32
Example-133:16
Quiz
Selection of Terms in G.P.3:00
Example-16:30
Example-27:04
Sum of n terms of a G.P.1:57
Use the gp sum formulas sn=a(r^n-1)/(r-1) or sn=(1-r^n)/(1-r) with r≠1; if r=1, sn=na, for the sum of the first n terms.
Example-11:23
Example-22:07
Example-37:08
Example-42:41
Example-52:08
Example-63:37
Example-73:10
Example-83:15
Example-93:32
Example-103:48
Example-113:51
Sum to infinity in a G.P1:22
Example-11:44
Example-22:18
Example-31:48
Example-45:23
Example-53:24
Example-67:57
Example-70:57
Example-82:57
Example-92:50
Example-103:57
Example-116:19
Example-122:58
Quiz
Properties of G.P.14:12
Example-14:05
Example-24:51
Show that for a, b, c in AP and x, y, z in GP, x^(b−c) y^(c−a) z^(a−b) equals 1, given y^2 = xz and 2b = a + c.
Example-33:08
Example-43:25
Example-56:39
Example-66:51
Example-710:21
Example-82:58
Example-92:52
Example-102:50
Insertion of Geometric Means between two numbers12:26
Example-14:12
Example-25:11
Find n so that (a^(n+1)+b^(n+1))/(a^n+b^n) equals the geometric mean sqrt(ab). The solution uses cross multiplication and factoring to show n = -1/2.
Example-34:27
Example-43:27
Example-58:14
Example-65:46
Example-74:36
Example-83:52
Example-95:27
Example-104:24
Example-111:45

Factorial Notations6:38
Example-12:23
Example-21:35
Example-32:16
Fundamental Principle of Counting7:51
Example-11:19
Example-22:29
Permutations6:04
An Important Theorem4:10
Example-11:35
Example-23:29
Apply the nPr formula to solve 2 times 5P3 equals nP4, rewrite with factorials, cancel terms, compare factors, and deduce n equals five.
Example-34:39
Example-44:27
Combinations4:30
Example-12:19
Example-22:23
Example-33:08
Compute the total number of committees of two, three, or four from ten people using combinations C(10,2), C(10,3), and C(10,4) to yield 375.
Example-43:35
Quiz

Requirements

Elementary knowledge of Math

Description

Welcome to Precalculus and Trigonometry!

We're thrilled to have you join this exciting course on Precalculus and Trigonometry! This journey will equip you with powerful mathematical tools that unlock a vast world of applications in science, engineering, and many other fields.

Here's what you can expect:

Exploring Complex Numbers: We'll delve into the fascinating realm of complex numbers, which extend beyond the familiar realm of real numbers.
Mastering Trigonometry: Trigonometry plays a central role in understanding relationships between angles and sides of triangles. We'll build your foundation in trigonometric functions.
Conquering Coordinate Geometry: Get ready to explore the intersection of algebra and geometry! Coordinate geometry allows us to represent points, lines, circles, and other shapes through their coordinates on a graph. Develop your skills in visualizing geometric objects using equations and manipulating them algebraically.

A Supportive Learning Environment:

We understand that learning can be challenging at times. That's why we encourage you to actively participate and ask questions! We have a dedicated Q&A forum where you can seek clarification and share your doubts with your instructor. Don't hesitate to ask for help – we're here to support your learning journey every step of the way.

Embrace the Challenge, Aim for Success:

Precalculus and Trigonometry are stepping stones to more advanced mathematics and pave the way for exciting careers in various fields. Embrace the challenges you'll encounter, and approach them with a positive attitude and a thirst for knowledge. Remember, hard work and perseverance are key ingredients for success!

We're confident that by actively engaging with the course material, participating in discussions, and taking advantage of the resources available, you'll gain a solid foundation in Precalculus and Trigonometry. We wish you all the best in your academic journey!

Who this course is for:

Those who wish to study precalculus and trigonometry

Precalculus and Trigonometry

What you'll learn

Explore related topics

Course content

Complex Numbers51 lectures • 5hr 25min

De-Moivre's Theorem17 lectures • 1hr 39min

Rational Expressions13 lectures • 1hr

Partial Fractions11 lectures • 1hr 15min

Functions11 lectures • 54min

Arithmetic Progressions48 lectures • 3hr 50min

Geometric Progressions65 lectures • 4hr 46min

Harmonic Progression25 lectures • 2hr 7min

Special Series Related with Natural Numbers6 lectures • 23min

Combinatorics18 lectures • 1hr 5min

Requirements

Description

Who this course is for: