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A Guide to Trigonometry for Beginners

Teaching Approach

When teaching trigonometry, start with a recap the theorem of Pythagoras followed by

defining the trigonometric ratios in a right angles triangle. A lot of examples are

recommended to ensure proper understanding in recognizing the opposite, adjacent and

hypotenuse sides. Triangles with the numerical length of sides and algebraic lengths of sides

are recommended.

The proper use of the calculator must be stressed. Learners must not be restricted to just

remembering the important keys, but a proper explanation of the reasoning behind pressing

the sin, cos and tan keys, compared to Shift sin, Shift cos and Shift tan. The responsibility

lies with the learners to ensure that their calculator is set in degrees.

Once learners are able to solve angles and sides in right angled triangles, the link to similar

triangles can be bridged. The important concept of sides in the same ratio does not affect

the angle. This concept can be further developed by using similar triangles to determine

angles and sides of triangles which otherwise would be difficult to determine. The following

example will illustrate this point:

We can use similar triangles to determine the height of the tree in the example

The shadow that a tree casts is used in the following way: we put a pole of a certain height

(example 2m) in the line of the shadow, we measure the distance from the tree to where the

shadow hits the horizontal (example 20m) and measuring the distance from the pole to

where the shadow hits the horizontal (8m), we can use similar triangles and trigonometric

ratios in the following way to determine the height of the tree:

In ABC : tan 2

8

In ADE : tan x

20

x 2 x 20 2

20 8 8

x 5m

Other uses of trigonometry and similar triangles must be highlighted to ensure learners see

the relevance of trigonometric definitions. Trigonometry and Similar triangles are used in

engineering, architecture, construction etc.

Hints on solving trigonometry problems:

If no diagram is given, draw one yourself.

Mark the right angles in the diagram.

Show the sizes of the other angles and the lengths of any lines that are known

Mark the angles or sides you have to calculate.

Consider whether you need to create right triangles by drawing extra lines. For example,

divide an isosceles triangle into two congruent right triangles.

Decide whether you will need Pythagoras theorem, sine, cosine or tangent.

Check that your answer is reasonable.

The hypotenuse is the longest side in a right triangle

Video Summaries

Some videos have a `PAUSE' moment, at which point the teacher or learner can choose to

pause the video and try to answer the question posed or calculate the answer to the problem

under discussion. Once the video starts again, the answer to the question or the right

answer to the calculation is given.

Mindset suggests a number of ways to use the video lessons. These include:

Watch or show a lesson as an introduction to a lesson

Watch of show a lesson after a lesson, as a summary or as a way of adding in some

interesting real-life applications or practical aspects

Design a worksheet or set of questions about one video lesson. Then ask learners to

watch a video related to the lesson and to complete the worksheet or questions, either in

groups or individually

Worksheets and questions based on video lessons can be used as short assessments or

exercises

Ask learners to watch a particular video lesson for homework (in the school library or on

the website, depending on how the material is available) as preparation for the next days

lesson; if desired, learners can be given specific questions to answer in preparation for

the next day's lesson

1. Introduction to Trigonometry

This video gives brief description of how trigonometry was first discovered and used. It

also describes the practical application of trigonometry through the theodolite, as used by

land surveyors.

2. Introduction to Sin, Cos and Tan

This video covers the fundamental definitions of the trigonometry. It explains that

trigonometry is ultimately the relationship between ratios of sides of triangles with respect

to an angle in that triangle.

3. Basic Use of Sin, Cos and Tan

In this lesson we will use sin, cos and tan ratios in right angled triangles. We start by

revising the definitions.

4. Using to Calculating a Side

This video covers the first of the application videos in which we use the trigonometric

ratios to determine the length of a side in a right angled triangle. The emphasis is on

choosing the correct trigonometric ratio.

5. Using Trigonometric to Calculate an Angle

This video covers the second of the application videos in which we use the trigonometric

ratios to determine the size of an angle, given at least two sides in the right angled

triangle.

6. Introducing Trigonometry on the Cartesian Plane

In this lesson we look at we will be looking at the trigonometric ratios on the Cartesian

Plane.

How to convert sin to Cos? sine function can be changed to cosine and vice versa by adding 90 degrees and its multiples in domain of function so Sin (a+90)= cos a it is +ve as in angle lies in 2nd quad if a is less than 90 and sine is + ve in 2nd quad 15.4K views View upvotes Related Answer Awnon Bhowmik , studied at University of Dhaka

Title: A Guide to Trigonometry for Beginners

Subject: A Guide to Trigonometry for Beginners

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