# Trig Calculator

'Make your very own trig ratio calculator!'

When you input sin 30 on your calculator you should get 0.5[1]Have you ever wondered what your calculator does to get that value? What process does it go through? What does sin 30 actually mean? Why is it always the same? In this activity, you will make your own trig ratio calculator that will give you the same results as your calculator. In doing so you will have to examine carefully the fundamental principles on which trigonometry is built. This should help give some meaning to the whole idea which, in turn, should help you master its application! Part of this activity is the careful, logical programming of a dynamic geometry file to achieve this!

### Aims

For students to extend their understanding of the geometric origins of the sine, cosine and tangent ratios by constructing the triangles that can be used to calculate them. This should help with the basic applications of the ratios to solve problems.

### Resources

This is a computer based activity and students will need access to dynamic geometry software. I recommend the free and easily downloadable  Geogebra. The task is outlined with video and text below! Teachers can read more with the  Trig calculator teacher's notes.

#### The goal!

The video below shows the final product and what it can do to help establish the aim of the task!

#### Key features

Either in small groups or as a whole class, spend some time considering the key features of the calculator and begin listing the elements you think are included and the order in which they will need to be made. The key question here is to think about how some things can be made variable! As a hint, it is worth knowing that there are some hidden construction lines that the triangle was drawn on top of. Good luck!

So now that you have a trig calculator to play with, use it to try some of the tasks below.

1 - Use the calculator to generate some values for sin x where x is the angle that you vary, and plot the graph of sin x for values of x between 0 and 90. Once the sign graph is done (you may have done so in a previous activity) repeat the procedure for cos x and tan x

– Consider the three functions sin x, cos x and tan x. Use the graphs you have drawn (it may be useful to plot them on the same set of axes) the consider the following questions

a)   What are sin 0 and sin 90? Can you offer an explanation for this?

b)   What are cos 0 and cos 90? Can you explain this in relation to your answer to the previous question?

c)   Explain what happens at tan 0 and tan 90

d)   For what value of x does sin x = cos x? Can you explain why

e)   Solve the equation (by using your graphs and/or your cabri calculators) cos x = sin 30

f)    Now solve sin x = cos 30

g)   Can you explain the solutions to the previous question?

#### How to build the calculator

The challenge of the task is seriously reduced if you watch this video straight away, so please have a good go yourselves before watching these videos.

1 - Making the triangle

2 - Measuring and calculating with the sides

This activity is relevant to section New - 5.2, Previous - 5.3 of the syllabus on right-angled trigonometry. Whilst many students will have previous experience of this concept, it is good to take a new look at it!

### Description

Here follows an outline of what the task is. If students are not reading this page then the teacher will need to show and give this overview.

• Show students a finished trig ratio calculator and show how its features can be changed.
• Explain that the task is for students to build one themselves by programming with dynamic geometry.
• Ask students to work in small groups or have a discussion so that the key features of such a construction can be discussed before students attempt to build their own.
• Allow students some time to play with this task. Teachers can decide to how much and when to help and this may eventually involve some whole class demonstration. All of this depends on students previous experiences of dynamic geometry. A 'How to' video is also provided for making the calculator using Geogebra.
• Students are then asked to use the calculators to investigate some patterns. For example, that for 0 to 90 cos is a reflection of sin and sin 30 = cos 60. These tasks are outlined in the brief worksheet.

### I did it my way!

As a practising maths teacher I know that most of us like to give activities our own little twist and do them 'our way'. It would be great to add a little collection of 'twists' from users. You can either add your twist to the comments section below or e-mail them directly to me at jamesn@inthinking.co.uk In time some of these twists may appear here....

#### Footnotes

• 1. Careful to make sure calculators are set to degrees and not radians.
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