Find The Exact Value of The Trigonometric Function – GCSE Maths

Step #1: Identify the Trigonometric function from given values.
Step #2: Plug the known values into the formula.
Step #3: Solve it.

Introduction

In GCSE Maths, you’re often asked to find sin, cos, or tan of specific angles without a calculator. These specific values are called exact trigonometric values.
Exact trigonometric values refer to the known and precise values of sine, cosine, and tangent for specific standard angles, without using a calculator.
These values are written as fractions or square roots, not rounded decimals.
We study exact trigonometric values to solve non-calculator GCSE exam questions accurately.

Example:

If we need to calculate exact values of sin, cos, or tan for special angles like 0°, 30°, 45°, 60°, or 90°, there’s no need for a calculator.
We can use a simple trigonometric values table that shows all the exact answers using fractions and square roots.

Let’s draw and understand the full table step by step:

First, we will find the value of sine, because using the sine values, we can also find the values of functions like cosine and tangent.
So, to start with this, first we will take the sine value and its corresponding angle on one side. Now, for each angle, we will take a number from 0 to 4, find its square root, and then divide it by 2, like-

Now, to find the value of tan, we will again use a method similar to sine. First, we will take the same numbers and find their square roots, but this time, instead of dividing by 2, we will divide by the reverse of these numbers.

After solving these values, we will get the tan values for each angle and tan(90°) is undefined because there is division by zero, which is mathematically impossible.