Trigonometry

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

Concept Map

[maximize][fold]

Textbook

1. Karnataka text book for Class 10, Chapter 12 - Trigonometry

For NCERT Text book Please click here
For Tamil Nadu Text book click here and here

Additional Information

Useful websites

1. To get Yakub Koyyur GHS Nada videos on Trigonometry in Kannada click here
2. Trigonometry on Wikipedia click here
3. Khan academy trigonometry video
4. For more about trigonometry click here
5. https://www.khanacademy.org/math/trigonometry%7C Trigonometry: khan academy
6. - fundamental concept of angle in trigonometry this web describes trigonometrical functions
7. Videos on Trigonometry from YouTube for basic ideas

1. Slide share about trigonometry and its application

Reference Books

For more details of trigonometry see these trigonometry reference books.

1. Text Book of Mathematics Pre university Karnataka Government
2. Trigonometry, I.M. Gelfand, Mark Saul
3. Trigonometry Refresher (Dover Books on Mathematics), A. Albert Klaf, Mathematics
4. Schaum's Outline of Trigonometry, 5th Edition, Robert Moyer, Frank Ayres
5. Trigonometry, 8th Edition, Ron Larson ($$$)
6. Advanced Trigonometry, by C.V. Durell, A. Robson

Teaching Outlines

History of Trigonometry

Learning objectives

1. Understanding of how trigonometry is developed
2. Understanding the contribution of Indians in the field of Trigonometry

Notes for teachers

Give information about the contribution of Indians in the field of Trigonometry to your children, it would help to develop an interest in development of Trigonometry.

Activities

Activity No.1 For History of Trigonometry click here
Activity No.2 For History of Trigonometry slide show click here

Angle Measurement

Learning objectives

• Understanding the units of measurement of an angle
• Understanding the interconversion units of measurement of an angle

Notes for teachers

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

Activities

1. Activity No #1 Introducing units of angle measurements
2. Activity No #2 Interconversion between degree measurement and angle measurement
3. Activity No #3 Angle of elevation and angle of depression

Introduction to Trigonometric Ratios

Learning objectives

• Identifying the opposite side, adjacent side, and hypotenuse of a right -angle triangle.
• Understanding the concept of different Trigonometric ratios.

Notes for teachers

Use property of similar triangle theorem for two similar right-angled triangles during development of trigonometric ratios.

Activities

Introduction to Trigonometric Ratios

1. Introduction to Trigonometry - Click here
2. Activity1_Basic Trigonometric ratios - click here

Trigonometric ratio with angles

Notes for teachers

Many teachers and students feel that Trigonometry is a difficult to understand subject. One reason for this is that Trigonometry is multi-concept based. A student should know following concepts well

1. of measuring-angles, triangle and right-angled triangle,
2. Pythagoras theorem,
3. ratios,
4. proportionality
5. Identities.
6. Trigonometry also require students insight, visualization, and perceptual ability.

Activities

1. Activity No #1- Trigonometry ratios - Click here

Application of Trigonometry

Notes for teachers

These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.

Activities

1. Activity No #1
2. Activity No #2

Hints for difficult problems

Problem-1

prove that ${\frac {1-\tan ^{2}A}{1+\tan ^{2}A}}=1-\sin ^{2}A$

Solution of this problem click here

Project Ideas

PROJECT 1.

Calculation of angle of elevation
Trigonometry is around us.In this project ,we will apply our knowledge of trigonometry to shadows in order to calculate the angle of elevation to the sun at different times of day.
Procedure of Project: To calculate the angle of elevation of the sun go through the procedure

• Measure your height and the length of the shadow you cast at two different times of day [at least 3 hours apart]
• Record the times and measurements [with units]
• Draw the right triangle in this scenario.
• Label the sides of your drawing with your measurements and angle of elevation
• Solve for the angle of elevation while clearly showing all your steps
  Note for teachers
  Don't forget that you need to do the procedure above twice two different times in a day.