3 Memorisation Tricks For Recalling Trigonometry Formulae

Trigonometry is a huge topic in secondary and JC math that is full of formulae to remember. From the basic ratios to trigonometric identities, mastering trigonometry means being able to recall and use these formulae on demand.

So, how do we help our tuition students remember everything? Mnemonics! Mnemonics are tools to help you remember something more easily – they could be an acronym, a humourous phrase, or a visual representation that triggers you to recall the actual formula.

Below, we will be sharing some of the mnemonics that our IP Math tutors use, as well as some other creative ones that are popular with students!

Trigonometric ratios

The sine, cosine and tangent ratios are one of the fundamental concepts you need to know in trigonometry. While these ratios will become easier to recall the more you do trigonometry questions, beginners will find having a mnemonic helpful. Here are some ways to recall the trigonometric ratios:

• TOA CAH SOH: Meaning ‘big-footed aunt’ in Hokkien, this mnemonic is taught by most Singapore math teachers and is very simple and catchy!
• “Silly Old Humans Can Always Have Their Own Answers”: Although it is longer, some people prefer having a catchy phrase like this to memorise the formula.
• Tan = Sin ÷ Cos: For the logical thinkers, this is really all you need. You can derive the other ratios from this, although it might be a little time-consuming to do this during the exam.

Signs of trigonometry functions in the quadrants of the plane

Another important thing to know is the sign of the trigonometric functions depending on which quadrant the angle is in. Most mnemonics help students remember this using the acronym ASTC, which stands for the functions that are positive in each quadrant. We also highly recommending making a quick sketch of the quadrants to help you visualise everything more clearly!

Quadrant 1 (0° < q  < 90°): All trigonometric functions are positive in this quadrant.

Quadrant 2 (90° < q  < 180°): Sine and cosecant functions are positive in this quadrant.

Quadrant 3 (180° < q  < 270°): Tangent and cotangent functions are positive in this quadrant.

Quadrant 4 (270° < q  < 360°): Cosine and secant functions are positive in this quadrant.

Some of the popular mnemonics that can help you remember these are:

• All Science Teachers (are) Crazy: this is great because it goes in order from the 1st quadrant to the 4^th quadrant, but it is slightly longer than the 1-word acronyms below.
• Add Sugar To Coffee: no extra words needed, and it goes in order from the 1^st to the 4^th
• ACTS: it’s a very simple word, but you need to remember that it starts from quadrant one and goes clockwise (not in the order of the quadrants).
• CAST: this is also a simple word but it starts from quadrant 4 and goes in the anticlockwise direction

Trigonometry hexagon

What if there was ONE diagram that could help you recall MANY of the trigonometric identities together? The wonderful thing about trigonometry is that it is built on ratios and patterns, so a lot of the trigonometric identities are inter-related.

Some teachers use this ‘magic hexagon’ to showcase the relationships between the trigonometric identities. You just need to remember the position of the 6 trig ratios (sine, cosine, tangent, cosecant, secant, and cotangent), and you have many of the important identities at your fingertips.

Here’s what it looks like:

Conclusion

Trigonometry might be a heavy topic with lots of formulae to remember, but knowing the formulae is not enough – students need to know how to apply them in the right situations.

That is why at Future Academy, our IP Math and JC Math tutors don’t just teach formulas – we teach students how to remember, how to apply, and how to stay calm under exam conditions. By combining strong conceptual teaching with effective memory techniques, we help students turn trigonometry from a memorisation-heavy topic into a manageable and fulfilling one.

If trigonometry has been a stumbling block for you or your child, join us for secondary math tuition in Singapore and turn this weakness into a strength!

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