# Textbook

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

## Useful websites

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.

## 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.

## 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.

## 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 ${\displaystyle {\frac {1-\tan ^{2}A}{1+\tan ^{2}A}}=1-\sin ^{2}A}$

# 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.