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"Mastering Trigonometry: Unleashing the Secrets of Triangles

High school math that covers Trigonometry and its Identities in detail - Unleashing the Secrets of Triangles and Beyond.

Created byLakshmi Narayana

Last updated 6/2023

English

What you'll learn

Review of Concepts Trigonometric Ratios.
Trigonometric Ratios of an acute angle of a right angled triangle.
Relation between Trigonometric Ratios.
Trigonometric Ratios of some specific angles.
Trigonometric Ratios of complementary angles.
Proofs of applications of Trigonometric Identities
Eliminating θ.

Course content

13 sections • 85 lectures • 8h 38m total length

Introduction11:36
Introduction
Q 18:18
Given tan A = 4/3, find the other trigonometric ratios of the angle A.
Q 29:08
If ∠B and ∠Q are acute angles such that sin B = sin Q, then prove that ∠B = ∠Q.
Q 35:47
Consider ∆ACB, right-angled at C, in which AB = 29 units, BC = 21 units and ∠ABC = θ (see Figure). Determine the values of
(i) cos^2θ + sin^2θ,
(ii) cos^2θ- sin^2θ.
Q 45:55
In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.
Test your understanding
Home Assignment

Introduction3:17
Relations between Trigonometric Ratios& Its applications.
Q 18:45
If θ is an acute angle and 3 sin θ = 4 cos θ, then find the value of 4 sin^2 θ – 3 cos^2 θ + 2.
Q 26:12
Prove that: cosA/(1+tanA) - sinA/(1+cotA)= cos A - sin A.
Q 32:49
If tan A + cot A = 2, then find the value of tan^2A + cot^2A.
Q 45:03
In ∆OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm (see Figure). Determine the values of sin Q and cos Q.
Test your understanding
Home Assignment

Introduction22:52
Trigonometric Ratios of Some Specific Angles
Q 10:53
The value of tan⁡〖〖30〗^0 〗/cot⁡〖〖60〗^0 〗 is
(A) 1/√2 (B) 1/√3 (C) √3 (D) 1
Q 22:58
Evaluate: sin2 30° cos^2 45° + 4 tan^2 30° + (1/2)sin^2 90° - 2 cos^2 90° + 1/24.
Q 32:22
If tan (3x + 30°) = 1 then find the value of x.
Q 43:03
If angles A, B, C of a ΔABC form an increasing AP, then find sin B.
Test your understanding
Home Assignment

Introduction2:30
Problems Based on Trigonometric Ratios of Some Specific Angles
Q 12:43
Evaluate: 4(sin^4(30°) + cos^4(60°)) - 3(cos^2 (45°)- sin^2(90°))
Q 23:16
Evaluate the following: (2cos^2 60^0+3sec^2 30^0-2tan^2 45^0)/(sin^2 30^0+cos^2 45^0 ).
Q 34:14
In ∆ABC, right-angled at B, AB = 5 cm and ∠ACB = 30° (see Figure). Determine the lengths of the sides BC and AC.
Q 42:32
In ∆PQR, right -angled at Q (see Figure), PQ = 3 cm and PR = 6 cm. Determine ∠QPR and ∠PRQ.
Test your understanding
Home Assignment

Introduction3:27
Trigonometric Ratios of Complementary Angles
Q 11:45
Evaluate(tan〖65〗^0)/(cot〖25〗^0 ).
Q 22:13
Evaluate (tan〖15〗^0)/(cot〖75〗^0 ) + (sin〖25〗^0)/(cos〖65〗^0 )
Q 32:41
Evaluate (tan〖50〗^0+sec〖50〗^0)/(cot〖40〗^0+cosec〖40〗^0 )+ cos40ocosec50o
Q 41:48
Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
Q 54:50
Find the value of (tan 1° tan 2° tan 3°…tan 89°).
Answer all questions for better practice
Home Assignment

Introduction2:09
Trigonometric Ratios of Complementary Angles - Continuation….
Q 14:27
If sin (A – B) = 1/2, cos (A + B) = 1/2, 0° < A + B ≤ 90°, A > B, find A and B.
Q 23:41
If sin 3A = cos (A – 26°), where 3A is an acute angle, find the value of A.
Q 33:42
In a triangle ABC, write cos ((B+C)/2)in terms of angle A.
Q 42:29
If A + B = 90° and sec A = 2/3, then find the value of cosec B
Q 52:39
If tan 2A = cot (A + 60), find the value of A where 2A is an acute angle.
Q 65:07
Show that: cosec^2θ - tan^2(90° -θ) = sin^2θ + sin^2(90° -θ)
Test your understanding
Home Assignment

Introduction5:49
Trigonometric Identities, Derivations, Conversion of Trigonometric Ratios in Terms of Other Trigonometric Ratios
Q 13:34
Express the ratios cos A, tan A and sec A in terms of sin A.
Q 24:14
Prove that sec A (1 – sin A)(sec A + tan A) = 1.
Q 36:34
Prove that: (sin θ + 1 + cos θ) (sin θ – 1 + cos θ). sec θ cosec θ = 2
Q 45:07
Prove that Sinθ/(1+cosθ ) + (1+cosθ )/(sinθ )= 2cosecθ
Test your understanding
Home Assignment

Introduction1:13
Trigonometric Identities& Problems Based on Trigonometric Identities
Q 15:13
Prove that (cotA-cosA)/(cotA+cosA) = (cosecA-1)/(cosecA+1)
Q 210:45
Prove that (sinθ-cosθ+1)/(sinθ+cosθ-1) = 1/(secθ-tanθ) using the identity sec^2q = 1 + tan^2q.
Q 36:41
Prove: (tanA+secA-1 )/(tanA-secA+1) = (1+sinA )/cosA
Q 46:43
Prove that tanθ/(1-tanθ)– cotθ/(1-cotθ)= (cosθ+sinθ )/(cosθ-sinθ).
Test your understanding
Home Assignment

Introduction1:26
Trigonometric Identities& Problems Based on Trigonometric Identities- eliminating theta
Q 19:51
Prove the trigonometric identity √((cosecA-1)/(cosecA+1)) + √((cosecA+1)/(cosecA-1)) = 2 sec A.
Q 24:51
If sin X + sin^2 X = 1, prove that cos^2 X + cos^4 X = 1.
Q 34:51
Evaluate sin A. cos A – (sinAcos(90^0-A) cosA )/(sec(90^0-A)) − (cosAsin(90^0-A)sinA )/(cosec(90^0-A))
Q 49:37
If cosec θ + cot θ = p, then prove that cos θ = (p^2-1)/(p^2+1).
Q 55:57
If a cos θ- b sin θ = x and a sin θ + b cos θ = y, then prove that a^2 + b^2 = x^2 + y^2.
Test your understanding
Home Assignment

Q 19:42
In ∆ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine :
(i) sin A, cos A
(ii) sin C, cos C
Q 25:59
In Fig. 8.13, find tan P – cot R.
Q 35:02
If sin A = calculate cos A and tan A.
Q 46:29
Given 15 cot A = 8, find sin A and sec A.
Q 56:53
Given secθ = 13/12 calculate all other trigonometric ratios.
Q 64:50
If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠ B.
Q 711:43
If cot q = 7/8, evaluate :
(i) ((1+sinθ)(1-sinθ))/((1+cosθ)(1-cosθ))
(ii) cot^2 θ
Q 89:40
If 3 cot A = 4, check whether (1-tan^2 A)/(1+tan^2 A) = cos^2A – sin^2A or not.
Q 99:15
In triangle ABC, right-angled at B, if tan A = 1/√3 find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C
Q 107:45
In ∆PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of
sin P, cos P and tan P.
Q 113:58
State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = 12/5 for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sinθ = 1/2 for some angle θ.

Requirements

Elementary knowledge of basic fundamental operations.
Each chapter is inbuilt with prerequisite knowledge classes where the child gets immense knowledge and a clear understanding of the chapters.

Description

This course is carefully designed to explain various topics in Trigonometry like Trigonometric Ratios, Trigonometric Ratios of some specific angles and Trigonometric Identities.
It has 85 lectures spanning more than eight hours of on-demand videos that are divided into 9 sessions. The course is divided into a simplified day-by-day learning schedule.
Each topic is divided into simple sessions and explained extensively by solving multiple questions. Each session contains a detailed explanation of the concept.
An online test related to the concept for immediate assessment of understanding.
Session-based daily home assignments with a separate key The students are encouraged to solve practice questions and quizzes provided at the end of each session.
This course will give you a firm understanding of the fundamentals and is designed in a way that a person with little or no previous knowledge can also understand very well.
It covers 100% video solutions of the NCERT exercises , with selected NCERT exemplars and R D Sharma.
Our design meets the real classroom experience by following classroom teaching practices. We have designed this course by keeping in mind all the needs of students and their desire to become masters in math. This course is designed to benefit all levels of learners and will be the best gift for board-appearing students. Students love these easy methods and explanations. They enjoy learning maths and never feel that maths is troublesome.

Topics covered in the course:

Review of Concepts of Trigonometry.
Trigonometric Ratios.
Relation between Trigonometric Ratios.
Trigonometric Ratios of some specific angles.
Trigonometric Ratios of complementary angles.
Trigonometric Identities.
Eliminating θ.

With this course you'll also get:

Perfect your mathematical skills on Trigonometric Ratios and Trigonometric Identities.
A Udemy Certificate of Completion is available for download.

Feel free to contact me with any questions or clarifications you might have.

I can't wait for you to get started on mastering the real number systems.

I look forward to seeing you on the course! :)

Benefits of Taking this Course:

On completion of this course, one will have detailed knowledge of the chapter and be able to easily solve all the problems, which can lead to scoring well in exams with the help of explanatory videos ensure complete concept understanding.

Downloadable resources help in applying your knowledge to solve various problems.

Quizzes help in testing your knowledge. In short, one can excel in math by taking this course.

Who this course is for:

This course has been designed for students of the Grade 10th CBSE, ICSE, SSC, GCSE, IGCSE, SAT, ACT, GRE, and other board-appearing students.
Students studying for the public or other competitive examinations.
Home-school parents are looking for extra support with the fundamentals.
Anyone interested in revising or learning the basics of mathematics should.
Students in junior high and high school/secondary schools.
Anyone who wants to proficient mathematics and the Trigonometric Ratios and Trigonometric Identities well.
Anyone who wants to study math for fun after taking a break from school.
It will also benefit schools who wish to run classes in the absence of a teacher and make learning fun for their students.
It will also benefit teachers and schools who wish to improve their teaching skills and make learning fun for their students.
For 11th, 9th, and 8th grade students, this will help as a bridge course.

"Mastering Trigonometry: Unleashing the Secrets of Triangles

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Course content

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Exercise 8.111 lectures • 1hr 21min

Requirements

Description

Who this course is for: