There are many ways that allow you to work out the values for the trigonometric ratios of the most common angles (0°, 30°, 45°, 60° and 90° ) . Here is one of them.
A final Note….
The above did not address the 3rd trigonometric ratio – Tangent. However given that we know that tan (θ) = sin( θ ) / cos( θ ); then we can use the above method to work out the tangent of these angles.