Question

calculate all trigonometric ratio for angle 30 and 60 geometrically

Answer 1

sin 0° = √(0/4) = 0sin 30° = √(1/4) = ½sin 45° = √(2/4) = 1/√2 = √2/2sin 60° = √3/4 = √3/2;cos 90° = √(4/4) = 1.
similarly you can find the other values as well:cos 0° = √(4/4) = 1cos 30° = √(3/4) = √3/2cos 45° = 1cos 60° = √(1/4) = 1/2cos 90° = √(0/4) = 0.tan 0° = 0tan 30° = √3/3tan 45° = √(2/4) = 1/√2 = √2/2tan 60° = √3tan 90° = not defined
sec 0° = 1sec 30° = 2√3/3sec 45° = √2sec 60° = 2sec 90° = not defined.
cot 0° = not defined.cot 30° = √3cot 45° = 1cot 60° = √3/3cot 90° = 0
csc 0° = not defined.csc 30° = 2csc 45° = √2csc 60° = 2√3/3csc 90° = 1.

Answer 2

Here are the derivations of trigonometric ratios of 30° & 60°. Hope it helps!