13.3 Trigonometric Values of Special Angles
13.3.1 The 45°-45°-90° Right Triangle
13.3.2 The 30°-60°-90° Right Triangle
13.3.3 Quadrantal Angles
13.3.4 Coterminal Angles
The exact values of the six trigonometric ratios (sine, cosine, secant, cosecant, tangent and cotangent) cannot be calculated for most angles. Nor can the exact value of an angle be calculated if one of these ratios is given. However, there are special angles that would lead us to a more convenient calculations of these ratios. Among the special angles, in degrees, are 30°, 45°, 60°, 90° and their multiples. In radians, the special angles are π/6, π/4, π/3, π/2 and their multiples.
The values of the six trigonometric ratios for these special angles can easily be derived using the two special right triangles: 45°-45°-90° or 30°-60°-90°, whichever is applicable. The acronym SOHCAHTOA can be used to calculate the three basic trigonometric ratios (SINE, COSINE and TANGENT) while the three remaining ratios (secant, cosecant and cotangent) can calculated by getting the reciprocal of cosine, sine and tangent respectively.