Foundation GCSE, Higher GCSE

How to remember exact sin, cos and tan values

If you’re studying for your maths GCSE, there are certain values of sine, cosine and tangent that you need to know off by heart. Luckily, in two of the three mathematics exams, you will be allowed to use a calculator, but in the non-calculator exam you will need to know the following common values:

sin(0)                    cos(0)                    tan(0)
sin(30)                  cos(30)                  tan(30)                          
sin(45)                  cos(45)                  tan(45)
sin(60)                  cos(60)                  tan(60)
sin(90)                  cos(90)

You’ll notice there’s one missing – it’s because there is no trigonometric ratio for tan(90). Try typing it into your calculator and see what happens!

Here I will show you a neat little trick to help you remember these common values off by heart.

Step 1:

Construct this table – with sin and cos as the row headings and the angles as the column headings. The values are going to go on the inside of the table.

GCSE maths trigonometry table

Step 2:

On the inside of the table, put the numbers 0, 1, 2, 3 and 4 like so…

Higher maths trigonometry table - Sin & Cos values

Step 3:

Square root each of the numbers.

Square root each of the Sin & Cos numbers

Step 4:

Now divide by 2.

Dividing the square root Sin & Cos values by 2

Step 5:

Simplify where possible.

Simplifying the trigonometric expressions

So that leaves us with our values for sin and cos.

A table of set Sic and Cos angle values

Now you’re probably wondering about tan.

Tan(x) = Sin(x) ÷ Cos(x), so tan values can be calculated by simply dividing sin by cos.

Calculating Tan values from Sin & Cos

*if you know your surds you’ll notice I have rationalised the denominator here because this is what your calculator will automatically do when you type in tan(30).

Also note that if we tried to use this to calculate Tan(90), we would be doing 1 divided by 0. We cannot divide by zero, hence there is no value of Tan(90).

So, the final values you need to know are shown in the table below.

A table showing Sin, Cos & Tan values for set angles

So there it is – a memorable step-by-step guide for remembering the exact values of sin, cos and tan that you need to know for your maths GCSE.

I hope you found that useful. To practice using exact sin, cos and tan values in a range of different GCSE-style questions, try our worksheet.

If you would like someone to go through this with you in person, book a free maths tutoring taster session.

Other posts

How to use triangles to remember exact sin, cos and tan values
If you’re taking the higher maths GCSE, there are certain values of …
A more efficient method for listing the factors of a number
In this blog I will show you the most efficient way to …
GCSE and A-Level Results 2021
Unfortunately due to the pandemic, GCSE and A-Level exams were cancelled again …
The Look-and-Say Sequence
In a previous blog I looked in more detail into “the daddy …
How to represent a recurring decimal as a fraction
What is a recurring decimal? Some decimal numbers are easy to deal …
Divisibility rules for numbers 7-12
Following on from the previous blog, which showed you a series of …
Divisibility rules for numbers 2-6
In this blog I will show you how you can easily check …
The Fibonacci Sequence and the Golden Ratio
We have previously touched upon Fibonacci sequences when discussing different types of …
The Problem with Solving Inequalities in GCSE Maths
In this blog, I will explain one of the most common mistakes …
5 things that make a good maths tutor
Following on from our previous blog on why university students make excellent …
Triangles in GCSE Maths
Triangles come up a lot in GCSE mathematics. And there are a …
A guide to trigonometry (SOHCAHTOA) – Part 2
In the last blog, I introduced a method for using trigonometry to …
A guide to trigonometry (SOHCAHTOA) – Part 1
Following on from the previous blog on Pythagoras’ theorem, this blog will …
Easy as Py – a guide to Pythagoras’ Theorem
a2 + b2 = c2.That’s Pythagoras’ theorem. What it says is that …
5 more maths magic tricks
Following on from the previous blogs about the number 6174 and the …
Distance, speed and time calculations
In this blog, we will look at distance, speed and time calculations …
GCSE Results 2020
Due to the Coronavirus pandemic, 2020 has not been an orthodox year …
5 reasons you should hire a home maths tutor
At Metatutor, we provide home one-to-one face-to-face maths tuition. In this blog, …
A guide to solving linear equations
In this blog, I will show you a method for solving linear …
Hailstone Numbers
In our blog we’ve already covered Kaprekar’s constant, as well as the …

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.