How To Find The Exact Value Of Tan

If you're studying for your maths GCSE, at that place are certain values of sine, cosine and tangent that you demand to know off by heart. Luckily, in ii of the three mathematics exams, you will exist allowed to use a calculator, just in the non-calculator examination y'all will need to know the following common values:

sin(0)                    cos(0)                    tan(0)
sin(30)                  cos(30)                  tan(thirty)
sin(45)                  cos(45)                  tan(45)
sin(threescore)                  cos(threescore)                  tan(60)
sin(xc)                  cos(90)

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

Here I will testify you a not bad little trick to help you call back these common values off by centre.

Stride one:

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.

Step 2:

On the inside of the table, put the numbers 0, one, 2, 3 and 4 similar so…

Step 3:

Foursquare root each of the numbers.

Pace 5:

Simplify where possible.

So that leaves the states with our values for sin and cos.

Now you lot're probably wondering about tan.

Tan(x) = Sin(x) ÷ Cos(x), and then tan values can be calculated by simply dividing sin by 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 y'all blazon in tan(xxx).

Besides note that if we tried to use this to summate Tan(xc), we would be doing 1 divided past 0. We cannot divide by null, hence at that place is no value of Tan(ninety).

So, the final values y'all need to know are shown in the table below.

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

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

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

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Source: https://metatutor.co.uk/how-to-remember-exact-sin-cos-and-tan-values/

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