Why are 30-60-90 or 45-45-90 right triangles not helpful on quadrantal angles?

Answer 1

30-60-90 and 45-45-90 triangles are not particularly useful for quadrantal angles because these angles (0°, 90°, 180°, and 270°) correspond to specific points on the unit circle where the sine or cosine values are straightforward (0, 1, -1). These points do not require the detailed relationships defined by the special triangles, as the values can be directly derived from the coordinates of the circle. Therefore, the unique properties of 30-60-90 and 45-45-90 triangles are unnecessary for determining the trigonometric values at these specific angles.