Question

Sin37° 45'= Sin25° 34'= Sin69° 17'= Cos37° 45'= Cos25° 34'= Cos60°17'=

Answer 1

1)0,6122173
2)0,431561
3)0,9353412
4)0,7906896
5)0,9020838
6)Скорее всего ты имел ввиду косинус 69 ° , но я напишу оба(6.1 - косинус с градусом 60, а 6.2 - косинус с градусом 69)
6.1)0,4957113
6.2)0,3537469

Answer 2

Let's calculate the values step by step:

1. For sin(37° 45'): We know that sin(a + b) = sin(a)cos(b) + cos(a)sin(b) Therefore, sin(37° 45') = sin(30° + 7° 45') = sin(30°)cos(7° 45') + cos(30°)sin(7° 45')

Using known values: sin(30°) = 0.5 and cos(30°) = √3/2

sin(7° 45') = sin(7.75°) ≈ 0.1354 and cos(7° 45') = cos(7.75°) ≈ 0.9908

Now, plug in the values: sin(37° 45') ≈ 0.5 * 0.9908 + √3/2 * 0.1354 ≈ 0.7278

2. For sin(25° 34'): Similarly, sin(25° 34') = sin(20° + 5° 34') = sin(20°)cos(5° 34') + cos(20°)sin(5° 34')

Using known values: sin(20°) ≈ 0.3420 and cos(20°) ≈ 0.9397

sin(5° 34') = sin(5.567°) ≈ 0.0963 and cos(5° 34') = cos(5.567°) ≈ 0.9953

Now, plug in the values: sin(25° 34') ≈ 0.3420 * 0.9953 + 0.9397 * 0.0963 ≈ 0.3420 + 0.0932 ≈ 0.4352

3. For sin(69° 17'): Using the same approach, sin(69° 17') = sin(60° + 9° 17') = sin(60°)cos(9° 17') + cos(60°)sin(9° 17')

Using known values: sin(60°) = √3/2 and cos(60°) = 0.5

sin(9° 17') = sin(9.283°) ≈ 0.1607 and cos(9° 17') = cos(9.283°) ≈ 0.9869

Now, plug in the values: sin(69° 17') ≈ (√3/2) * 0.9869 + 0.5 * 0.1607 ≈ 0.8418

4. For cos(37° 45'): We know that cos(a + b) = cos(a)cos(b) - sin(a)sin(b) Therefore, cos(37° 45') = cos(30° + 7° 45') = cos(30°)cos(7° 45') - sin(30°)sin(7° 45')

Using known values: cos(7° 45') ≈ 0.9908 and sin(7° 45') ≈ 0.1354

Now, plug in the values: cos(37° 45') ≈ √3/2 * 0.9908 - 0.5 * 0.1354 ≈ 0.8540

5. For cos(25° 34'): Similarly, cos(25° 34') = cos(20° + 5° 34') = cos(20°)cos(5° 34') - sin(20°)sin(5° 34')

Using known values: cos(20°) ≈ 0.9397 and sin(20°) ≈ 0.3420

Now, plug in the values: cos(25° 34') ≈ 0.9397 * 0.9953 - 0.3420 * 0.0963 ≈ 0.9336

6. For cos(69° 17'): Using the same approach, cos(69° 17') = cos(60° + 9° 17') = cos(60°)cos(9° 17') - sin(60°)sin(9° 17')

Using known values: cos(9° 17') ≈ 0.9869 and sin(9° 17') ≈ 0.1607

Now, plug in the values: cos(69° 17') ≈ 0.5 * 0.9869 - (√3/2) * 0.1607 ≈ 0.3423

Now, let's summarize the results:

• sin(37° 45') ≈ 0.7278
• sin(25° 34') ≈ 0.4352
• sin(69° 17') ≈ 0.8418
• cos(37° 45') ≈ 0.8540
• cos(25° 34') ≈ 0.9336
• cos(69° 17') ≈ 0.3423

It's important to note that trigonometric values are approximate, and the actual values may have a few more decimal places, but these are sufficient for most practical calculations.