# Trigonometric Functions & Graphs: How to Revise

Updated: Nov 21

Trigonometric Functions & Graphs is one of the most *under-appreciated topics* on the Leaving Cert paper.

It is rarely mentioned amongst the heavy hitters like Calculus or Inferential Statistics.

But if you look at Tip #6 below, it appears in some shape of form, at least once every, in both Paper 1 AND Paper 2!

This post goes through some of the highlights of the Tacit Maths worksheet on Trigonometric Functions & Graphs, and some tips on how to approach it.

**FREE Sample:** In Tip #7, two "perfect" sample LCHL questions are highlighted. Students can try them out, and for teachers, the Powerpoint solutions are available for **free**.

**The Worksheet (Click to Download)**

## How To Revise

The Tacit Maths revision worksheet on Tacit Maths is over 20 pages long.

Here are a few things you should be focusing on:

**1. Geometry V Calculus**

Worksheet: n/a

Powerpoint: Pg 2

Any time I survey students on the topic they are most concerned about they almost always mention "Trigonometry".

However, they nearly always are fine with the Triangles/Geometry aspect of Trig.

It's almost always Trigonometric Functions & Graphs that they are referring to.

I think it's important to distinguish the difference between the two.

You can treat them as two completely separate chapters!

**2. Trig Equations: Full Example**

Worksheet: Pg 2

Powerpoint: Pg 4-5

Very often, when revising this topic, students only need to be reminded of a full example of how to solve a Trigonometric Equation.

The first page of the worksheet contains such an example.

** Tip:** If you are overwhelmed by this example, don't panic! Each step will be covered in more detail in the following pages.

**3. Radians: Working with Fractions**

Worksheet: Pg 9

Powerpoint: Pg 43-46

Students are almost always turned off by Radians. Interestingly however, the main problem here is students ability to work with FRACTIONS.

** Top Tip:** Start your revision of Radians with this fractions exercise (without using calculators!). All the techniques used here are what is needed to tackling radians.

**4. Radians: Working with Decimals**

Worksheet: Pg 11 - 12

Powerpoint: Pg 54 - 70

If you analyse the LCHL exam questions, most questions involve the "special angles" (i.e. 30, 45 and 60).

However, a huge amount of the harder Part B questions involve decimals (like in the examples shown here).

I used to skip through this section before, but in recent years I've found that it's one of the most important exercises on the worksheet.

**Warning: **Before you tackle this exercise with decimals, you need to know the steps/method of solving "regular" Trig Equations inside out.

**5. Trig Functions & Graph Intro**

Worksheet: Pg 14

Powerpoint: Pg 54 - 70

The first page of the Functions & Graphs section (Section 3) is quite intense.

However, this is only an overall recap.

The details of the 4 Key Features are elaborated on in more detail in the following sections.

Use this page as revision tool when practicing exam questions.

**6. Recent Appearances**

As mentioned in the intro, Trig Functions and Graphs can come up in many shapes or forms.

It most often comes up as a Calculus questions. But it can also come up as a a question on it's own, or with Trigonometric Identities.

A question on Trigonometric Functions & Graphs has appeared in the following years:

#### Feel FREE to download a PDF of this Checklist here:

**7. Two Perfect Exam Questions **

What follows are two recent exam Questions (25 Mark and 50 Mark question).

**For students:** Feel free to download the free worksheet attached below. You can then look at the worked solution on our Youtube channel linked below,.

**For Teachers:** The Powerpoint solutions to these questions are attached below. Feel free to use this with your students.

(Click to view Powerpoint solutions and PDF of worksheet)

**(Part A) **

**Leaving Cert 2014 Paper 2 - Question 5 **

Worksheet: Pg 27

Powerpoint: Pg 165 -166

This is a great little question that assesses:

1. Your ability to plot Trig Functions on graphs.

2. Your understanding of how functions in general work.

3. Your ability to solve Trigonometric equations.

**Note:** I have made a Youtube video going through this exam question (click button).

**The Perfect Exam Question (Part B) **

**Leaving Cert 2017 Paper 2 Question 9**

Worksheet: Pg 20 - 21

Powerpoint: Pg 140 -144

This would be one of the more difficult questions on this topic in recent years.

It assesses:

- Your ability to draw Trig Functions,

- Your understanding of the Key Features of a Trig Function (i.e. midline/range/period).

- Your understanding of the a, b and c variables in the Trig function.
**Note: **The solution to this module is available to students in the 3rd eLearning Module in this page.

If you have any other comments/feedback on the Trigonometric Functions & Graphs module, or wish to gain access to the modules, by all means send me an email!

Diarmuid