Why We Need to Memorise Exact Values in Mathematics

Let's face it. Maths is dry. Your teacher probably reads off the textbook and works through problems in a monotonous voice. You're sitting there wondering...

"Why do we need to memorise this?"

Exact Values in Trigonometry falls into the category of things you learn once, forget, and then painfully relearn before exams. In reality, memorising Exact Values is far more useful than it first appears.

A Familiar Example: Times Tables

Think back to learning the 12×12 times tables. At the time, it felt repetitive and unnecessary. You were forced to memorise numbers without fully understanding why.

Fast forward to now and you probably don't even realise you're using them.

Exact values play the same role in trigonometry. Once memorised, they quietly work in the background while you focus on the actual problem.

The Building Blocks of Trigonometry

As you move through secondary maths, especially from Year 10 into Years 11 and 12 Methods, you will encounter Circular Functions such as sine, cosine, and tangent. These functions are rarely used on their own. Instead, they appear in equations, identities, graphs, and later, calculus.

Despite all this complexity, everything is built on a surprisingly small set of core angles between 0° and 90°:

• 0°
• 30°
• 45°
• 60°
• 90°

These are known as special angles. I've been tutoring maths for a long time, the best way to explain this to students is to think of these angles as sitting in the "memorisation zone." Learn these once, and you reuse them forever.

Small Effort, Big Payoff

Here's the fun part: memorising just five angles gives you access to many more.

Angles like 120°, 135°, 150°, 225°, and even negative angles all reduce back to the same exact values using reference angles and symmetry. It's like learning five passwords that somehow unlock the entire system.

Just a quick disclaimer, Exact Values help speed up your tech-free questions. For tech-active questions, you'll most commonly be dealing with decimal answers, that's a different story.

Speed, Accuracy, and Fewer Headaches

When exact values are memorised:

• You solve problems faster
• You make fewer algebraic errors
• You spend less time second-guessing yourself
• Exams feel more manageable

Instead of stopping mid-question to work out basic values, your brain can focus on strategy and method which is where marks are actually earned.

A Head Start That Compounds

If you memorise exact values in Year 10, you will notice a clear advantage in Years 11 and 12 Methods. Trigonometric equations, identities, graphs, and calculus applications become far less intimidating when the fundamentals are automatic.

In short, memorising exact values is not about rote learning for its own sake. It is about building a mental toolkit that makes higher-level mathematics faster, cleaner, and more confident. Just like times tables once did.

The future you will thank you for memorising Exact Values. Now go and play this game!