TrigonometryTrigonometryA New Angle On Maths!

The Clue is in the name...

“Tri...” - to do with triangles

“...metry” - to do with measuring

So Trigonometry is basically the study of triangles.

What is “Trigonometry”?

For our purposes, trigonometry deals with the relationships between the sides and angles of a triangle.

The trigonometry of right-angle triangles (those with one 90 degree angle) forms a key study area and is a powerful measurement tool across many different fields.

Trigonometry forms a basis for other areas of maths, like circular functions, complex numbers and polar coordinates.

It is essential to physics and astronomy, earth sciences, engineering, electronics, architecture and design, medical sciences, biology chemistry, computer graphics and game development!

We also use trigonometry in navigation and surveying land, and wouldn’t have GPS and mobile phones without it!

Characteristics of triangles

We know triangles have 3 sides and 3 internal angles.

Need to have a system for naming sides in relation to each other and the angles between them.

What are we interested in?We’re interested in the ratios of the sides and how they relate to the internal angles of the triangle.

From there we can work out and use a system of rules that applies to these ratios for all right hand triangles.

More on that later...

Start with the basics...What do you already know about triangles?

What next?Task 1: Measuring angles worksheet

Use a protractor to measure the angles

Task 2: Open up the blog, read through and complete the questions on Identifying sides in right angled triangles

Similar Triangles

Watch out!While the orientation of the triangles doesn’t stop them from being similar, you need to watch out that you have the right corresponding sides and angles.

It might help to redraw all the same triangles with the same orientation to begin with!

Lets see an example...

TrigonometryTrigonometryLesson 2Lesson 2

Today’s objectives...

Revisit what we discussed on Tuesday

Naming sides of right-angle triangles (also known as “right triangles”)

Similar Triangles

Investigate and explore trigonometric ratios

Use sci. calculator to calcuate trig ratios

What is Trig?

Study of triangles

We are interested in the relationship between the angles and sides of right angle triangles.

Need to be specific about which angles and sides we’re talking about in relation to each other.

We can also refer to these sides as H, O and A

Hypotenuse

focus angle

Opposite

Adjacent

H O

A

Similar TrianglesHow can we can tell if triangles are similar?

1. All of the angles are the same

2. The ratios of any corresponding sides are the same on both or all triangles.

Remember: Triangles are not always drawn to scale so don’t rely on your eyes! (Though sometimes they’re a good place to start...)

Are the triangles similar?

YES: Two angles are the same and as all angles sum to 180, all three must be the same.

Set up the ratios of corresponding sides

Need to work out which sides are corresponding.

two have hyp. and one other side - compare those first.

Therefore B and C must be similar.

Check to see if A is similar too - not always to scale!!

What now?Work through the “Discovering Trigonometry Worksheet”

Pick four triangles to investigate for each question

Copy out the table for each triangle in each question (thats 12 tables!)

And then?Bring up the blog on your computer and click on activity 4

Watch the video on the page and think about how the ratios you just calculated tie-in to the trigonometric functions explained in the video