Question

Sin54градусовsin18градусов

Answer 1

$sin54 \times sin18 = \frac{sin54 \times sin18 \times 2cos18}{2cos18} = \frac{sin54 \times sin36}{2cos18} = \frac{sin(90 - 36) \times sin36}{2cos18} = \\ \\ = \frac{cos36 \times sin36}{2cos18} = \frac{0.5sin72}{2cos18} = \frac{0.5sin(90 - 18)}{2cos18} = \frac{0.5cos18}{2cos18} = \\ \\ = \frac{0.5}{2} = 0.25$
Ответ: 0.25

Answer 2

To find the value of the expression "sin(54 degrees) * sin(18 degrees)," you can use the trigonometric identity:

sin(A) * sin(B) = (1/2) * [cos(A - B) - cos(A + B)]

In this case, A = 54 degrees and B = 18 degrees. Let's calculate it step by step:

1. Convert degrees to radians: A = 54 degrees * (π/180) ≈ 0.94248 radians B = 18 degrees * (π/180) ≈ 0.31416 radians

2. Substitute the values into the identity: sin(54 degrees) * sin(18 degrees) = (1/2) * [cos(0.94248 - 0.31416) - cos(0.94248 + 0.31416)]

3. Calculate the cosine values: cos(0.94248 - 0.31416) ≈ cos(0.62832) ≈ 0.80115 cos(0.94248 + 0.31416) ≈ cos(1.25664) ≈ 0.30902

4. Substitute back into the expression: sin(54 degrees) * sin(18 degrees) ≈ (1/2) * (0.80115 - 0.30902) ≈ 0.24607

Therefore, sin(54 degrees) * sin(18 degrees) is approximately 0.24607.