Introduction to Trigonometry

1, sin 45°/cos 45°, (√2/2)/(√2/2)

tan 45° = 1. Also, tan θ = sin θ/cos θ, so tan 45° = sin 45°/cos 45°. Since sin 45° = cos 45° = √2/2, we have tan 45° = (√2/2)/(√2/2) = 1.

1

By the fundamental trigonometric identity, sin²θ + cos²θ = 1 for any angle θ. This is true for θ = 30° as well. We can verify: sin 30° = 1/2, cos 30° = √3/2, so sin²30° + cos²30° = (1/2)² + (√3/2)² = 1/4 + 3/4 = 1.

0.6

Using sin²A + cos²A = 1: sin²A + (0.8)² = 1, so sin²A + 0.64 = 1, therefore sin²A = 0.36, so sin A = 0.6 (positive since A is acute).

sin 0° = 0, cos 90° = 0, sin 90° = 1, cos 0° = 1

From the standard values: sin 0° = 0, cos 0° = 1, sin 90° = 1, cos 90° = 0, and tan 0° = 0 (not 1).