Question

Sin7°30'cos7°30'cos15°

Answer 1

Відповідь:

1/8

Пояснення:

sin2a = 2sina*cosa  - формула, которую мы здесь используем

sin7°30'cos7°30'cos15°

Для удобства откинем cos15° сначала:

(sin7°30'cos7°30' * 2) / 2 = $\frac{sin(2*7°30')}{2}$ = sin15° / 2

возвращаем cos15° и повторяем процес

sin15° * cos15° / 2

(sin15 * cos 15 * 2) / 2 / 2

sin30 / 4 = (1/2)/4 = 1/8

Answer 2

To calculate the expression sin(7°30')cos(7°30')cos(15°), you can use trigonometric identities and the angles given in degrees and minutes. First, convert the angles from degrees and minutes to decimal degrees:

7°30' = 7 + 30/60 = 7.5 degrees 15° = 15 degrees

Now, plug these values into the expression:

sin(7.5°)cos(7.5°)cos(15°)

Next, you can use the trigonometric identity: sin(2θ) = 2sin(θ)cos(θ)

Apply this identity to the expression:

sin(7.5°)cos(7.5°)cos(15°) = 2sin(7.5°/2)cos(7.5°/2)cos(15°)

Now, calculate the values of sin(7.5°/2) and cos(7.5°/2):

sin(7.5°/2) = sin(3.75°) cos(7.5°/2) = cos(3.75°)

Using a calculator or trigonometric tables, you can find the approximate values of sin(3.75°) and cos(3.75°).

sin(3.75°) ≈ 0.0654 cos(3.75°) ≈ 0.9978

Now, plug these values back into the expression:

2sin(7.5°/2)cos(7.5°/2)cos(15°) ≈ 2(0.0654)(0.9978)cos(15°)

Now, calculate cos(15°):

cos(15°) ≈ 0.9659

Finally, plug this value back into the expression:

2(0.0654)(0.9978)(0.9659) ≈ 0.1267

So, sin(7°30')cos(7°30')cos(15°) is approximately equal to 0.1267.