Question

Доказать, что sin 30° = , cos 60° =

Answer 1

Ответ:

Sin30=1/2 и cos 60=1/2

Объяснение:

Answer 2

To prove that sin 30° and cos 60° have specific values, we can use the trigonometric identities. Let's go step by step:

1. First, we need to recall the values of sine and cosine for some basic angles:

• sin 0° = 0

• sin 30° = 1/2

• sin 45° = √2/2

• sin 60° = √3/2

• sin 90° = 1

• cos 0° = 1

• cos 30° = √3/2

• cos 45° = √2/2

• cos 60° = 1/2

• cos 90° = 0

Now, let's prove the two trigonometric values you asked for:

1. Proving sin 30° = 1/2: We can use the fact that sin 30° is half of sin 60°. So, we write: sin 30° = 1/2 * sin 60°

Now, we know that sin 60° is √3/2, so we get: sin 30° = 1/2 * (√3/2) = √3/4.

Therefore, sin 30° = √3/4 ≈ 0.866.

2. Proving cos 60° = 1/2: We can use the fact that cos 60° is equal to sin 30°. So, we write: cos 60° = sin 30°

We already calculated sin 30° above, which is √3/4.

Therefore, cos 60° = √3/4 ≈ 0.866.

To summarize:

• sin 30° = √3/4 ≈ 0.866
• cos 60° = √3/4 ≈ 0.866

Both of these values are equivalent and can be approximated to approximately 0.866.