Question

If the sin 90° = 1, then which statement is true? (4 points)

cos 0° = 1, because the angles are complements

cos 90° = 1, because the angles are supplements

cos 0° = 0, because the angles are complements

cos 90° = 0, because the angles are supplements

Answer 1

To determine which statement is true, let's analyze them based on trigonometric identities.

1. **sin 90° = 1** - This is correct, as given.

2. **cos 0° = 1, because the angles are complements** - This is true. The complement of 0° is 90°, and cos 0° = 1.

3. **cos 90° = 1, because the angles are supplements** - This is false. The supplement of 90° is 90° itself, and cos 90° = 0.

4. **cos 0° = 0, because the angles are complements** - This is false. We already established that cos 0° = 1.

5. **cos 90° = 0, because the angles are supplements** - This is true, as cos 90° indeed equals 0, but the reasoning regarding supplements is irrelevant here.

Based on this analysis, the following statements are true:

1. **cos 0° = 1, because the angles are complements.**
2. **cos 90° = 0.**

The most correct statement, fitting the criteria asked in your question, is:

**cos 0° = 1, because the angles are complements.**