Ratios for Special Right Triangles
Refer back to these special right triangles.
- Calculate the sin and cos ratios for the 30 degree angles in each triangle and compare.
- Repeat the process for the 60 degree angle in each triangle. Compare the sin and cos ratios for the 60 degree angle.
- Next, calculate the sin and cos ratios for the 45 degree angles in the following triangles:
- Explain why the sin and cos ratios for congruent angles are all the same regardless of the size of the triangle.
- Then compare the sin, cos and tan values for the 30 degree angle to those for the 60 degree angle, and the 45 degree angles using the following table:
| Angle (Θ) | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|
| 30° | ||||||
| 60° | ||||||
| 45° |
Circle the congruent ratios, one at a time, to see a pattern.
- Which ratios are the same? Which are reciprocals? Write 3 statements to summarize the connections between the ratios.
- What is your method for remembering the trigonometric ratios?