# Trig Calculator - TN

### Teacher's Notes

When students simply use a calculator, the meaning behind trig ratios is quickly lost. In order to build the ‘cabri – calculator’ students are challenged to really understand the origins of the ratios. The plotting of these ratios as a function reinforces the patterns that exist in the relationship between 2 variables and gives a context for calculating a number of the ratios. In Part 3 students are asked to relate the patterns they find to the physical situation of the geometry and this is a critical link to make. These questions are all problems that can be solved with a variety of approaches and as such accessible to more students.

### How

The following is some practical advice about how the activity might be run.

#### Resources provided

The activity page offers a video demonstration that defines the task along with a series of related tasks and questions for students to do. These are aimed at helping students construct the calculator and then to use it. In addition there are also a couple of videos that explain how the calculator can be made using Geogebra.

#### Resources needed

Students will obviously need access to computers for this activity. Previous exposure to dynamic geometry is really helpful.

#### Time needs

This can usually be done in 1 hour, but depends largely on previous experience and the amount of input the teacher decides to give.

#### Starting and finishing

Time and ambition are key here. Left to students alone, this activity represents a big challenge, perhaps the teacher might consider that for some students, whilst choosing to orchestrate a group input for others. Students could be provided with partially completed tables and axes. A teacher may even decide to provide the students with the 'calculator’ in advance. As such the depth to which this activity is taken is very flexible.

#### Records

Its great if students manage to create the calculator themselves and this then provides an excellent record of the activity.

### What to Expect

• As mentioned already, much depends on previous experience students have of using dynamic geometry. If this is not very much then teachers will find themselves leading large parts of this activity.
• It is really important for students to get some experience of actually constructing the dynamic situation and watching what happens as the variables are changed. Giving students the pre-prepared file will not have the same effect.
• When students check that their calculator gives the same result they find it quite empowering and a real sense of understanding is given to the concept of trigonometry and this is invaluable.

### More

This activity is a great start to the trigonometry element of the unit and can be nicely followed up with the activity  rearranging relations.

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