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