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.

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