GCSE Maths Trigonometry for Beginners

Any student knows that when they have to sit there mathematics exams at school or college you are going to be presented with the Trigonometry questions , you will also have figured out by the time you finished your mock exams that these trigonometry questions hold a significant score in your exams, so its worth the little extra effort to learn this one!

Mathematics Can Be Fun! Yes it can and it can be fun for you as well, if you find that you don’t get it or are struggling its only because the method you are using does not work for you, it might work for someone else but it may take a different method or approach for you, so don’t be to hard on yourself because you can do it!

A Brief History of Trigonometry

Trigonometry was first used by the ancient Greeks and they called it Trigonon which simply means Triangles, they had figured out how to use a right angled triangle and its measurements also called Metron in ancient Greek, then they cleverly used this formula to measure the distance between the Earth and the Sun.

Trigonometry and the Triangle

Lets start by familiarising ourselves with the Triangle in question, it has a right angle that always has a fixed sum of 90 degrees, it also has three sides that are called the Opposite, Adjacent and the Hypotenuse which is the longer side of the three.

Lastly we are left with the Angle that is always opposite the side we call the ‘Opposite’ and sits adjacent to the side we call the ‘Adjacent’, simple enough don’t you think?

An easy word for remembering the formulas

An easy and tested method for remembering the formulas needed to calculate in Trigonometry is a word called “SOHCAHTOA” that’s “SOH-CAH-TOA”.

It basically gives you the complete set of equations and if you can remember this then you are only one more step away from completely cracking this theory, seriously now you will crack it!

Lets begin by starting with a question as seen in image (1.a)

We are presented with a right angled triangle and are given a length of 5m for the Adjacent side also we have a sum for the Angle of 60 degrees. We are now left with a question mark for the sum of the Opposite side.

Now to make life easier let’s dissect this question and just take out the facts we need to look at also to lay them out in a methodical manner:

• Adjacent (A) = 5m
• Opposite (O) = ?
• The Angle = 60

• Now all we need to do is select the right equation from our easily remembered word called “SOHCAHTOA”

• We have the Adjacent, the Angle and we need to find the value for the Opposite, so that’s our three indicators there!

• Now just have a look at the three possible equations and just match our findings to one of them.

• That’s it now you have the right equation to help you calculate the right answer.

• Lastly all we need to do now is to transpose (arrange) the equation so we are presented with the value for the Opposite side, its really that simple.

Transposing the Equation

This is more simple then you think honestly, once you have cracked the method for transposing an equation you will always be able to find the values you are looking for and calculate any question presented to you, once you have mastered this, Mathematics becomes so easy as you will see.

• Use an imaginary cross to separate the formula into four sections as seen in image step.1 here to the right.

• Now let’s begin to rearrange this formula step by step.
• The rules are simple: What is up must go down and what is down must go up, what we need must go to the left grid and the equal’s sign never moves!
• Now we need the value for the opposite so we take the opposite and place it to the left.
• Because the opposite is in the upper grid it must go down.
• Stick with it because this is really easy.

• We need to move the Tan.

• Tan is in the up and must go down.

• We don’t need the Tan so it goes to the right grid.

• Starting to sound easy now?

• Just flip it over so to speak like a reversal or lift it up, what ever is easiest for you to remember.

• And now we have transposed (arranged) our formula that will now give us a calculation for the opposite, didn’t I tell you this was easy?

• You can use this method to transpose other formulas too.

• Just a note for those that may not know? When two values are side by side as in this image, it means you must multiply and if they are over each other it means divide.

Now all we need to do is bring this all together and calculate the answer or value for the Opposite side, so I will run through the whole process in a quick methodical manner, starting with the question again.

Lets begin by starting with a question as seen in image (1.a)

We are presented with a right angled triangle and are given a length of 5m for the Adjacent side also we have a sum for the Angle of 60 degrees.

We are now left with a question mark for the sum of the Opposite side.

Now to make life easier let’s dissect this question and just take out the facts we need to look at also to lay them out in a methodical manner:

• Adjacent (A) = 5m
• Opposite (O) = ?
• The Angle = 60

Now to Choose The Right Formula

• Now all we need to do is select the right formula from our easily remembered word called “SOHCAHTOA”

Now Transpose The Equation

Use the easy method to transpose the formula so you can find the value for the Opposite as shown through images transposing equations steps 1 - 5.

Now we have the values laid out in order and have correctly chosen the formula plus transposed it to help calculate the value for the Opposite Side, all we have left to do is the maths.

• Using a calculator simply enter the value of the angle, so 60 degrees
• Then using the Tangent button abbreviated on the calculator as TAN you will be given a value of 1.7320
• This is the converted value for the angle using Tan.
• Now all we need to do is multiply by the adjacent value of 5.
• Which now leaves you with the value for the Opposite Side?
• So the long awaited answer is 8.66m
• Opposite = 8.66m

Don't Have a Calculator?

Then not to worry the clever people at NASA have made a conversion table for you to refer too, here is the link:

http://www.grc.nasa.gov/WWW/K-12/airplane/tabltan.html