How do I remember the trigonometric ratio values for 0°, 30°, 45°, 60° and 90°?

There is a neat pattern for sine. Write the numbers 0, 1, 2, 3, 4 for the angles 0°, 30°, 45°, 60°, 90°. Divide each by 4, then take the square root. So sin values become √(0/4), √(1/4), √(2/4), √(3/4), √(4/4), which give 0, 1/2, 1/√2, √3/2, 1. For cosine, just reverse the same list: 1, √3/2, 1/√2, 1/2, 0. For tangent, divide sine by cosine at each angle, giving 0, 1/√3, 1, √3, and undefined at 90°. Once you reconstruct the sin row this way, everything else follows. With a little practice you can rebuild the whole table in under a minute during the exam.