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A Guide to Trigonometry for Beginners
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
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
In ADE : tan x
x 2 x 20 2
20 8 8
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
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
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
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
6. Introducing Trigonometry on the Cartesian Plane
In this lesson we look at we will be looking at the trigonometric ratios on the Cartesian
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
Author: Microsoft® Office Word 2007
Creator: Microsoft® Office Word 2007
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