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

Question

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.