Exact Trig Values

Note that the values of sin θ going from 0° to 90° match those of cos θ going from 90° to 0°

Draw an equilateral triangle where the length of each side is 2
- Each angle will be 60°
Halve the triangle to form a right-angled triangle where one of the lengths is now 1
- One angle will now be 30°
Find the length of the missing side using Pythagoras
Use SOHCAHTOA to find the exact values of the trig ratios for 30° and 60°

Exact Values Notes Diagram 2

Draw an isosceles right-angled triangle where the length of the equal sides is 1
- The two equal angles will be 45°
Find the length of the missing side using Pythagoras
Use SOHCAHTOA to find the exact values of the trig ratios for 45°

5-4-2-exact-values-notes-diagram-1

If you forget the exact values in your exam
- Use a value that you think it could be
- Even if the value you used is incorrect, you will still get method marks for the rest of the question

The following diagram is not drawn to scale.

exact-trig-values-we

Without using a calculator, find the value of $x$ .

You have the hypotenuse and the side that is adjacent to the angle
Use CAH

$\cos (60) = \frac{x}{24}$

Multiply both sides by 24

$x = 24 \times \cos (60)$

Use $\cos (60) = \frac{1}{2}$

$x = 24 \times \frac{1}{2}$

$x = 12$

Exact Trig Values (Edexcel GCSE Maths: Foundation)