Question

Sin (π\10)*sin (3π\10) * cos (π\3)

Answer 1

Ответ:

sin(π/3)sin(3π/10) /2 или ≈ 0.125

Пошаговое объяснение:

Answer 2

To simplify the expression sin(π/10) * sin(3π/10) * cos(π/3), you can use trigonometric identities.

Recall the following identities:

1. sin(π/3) = √3/2
2. sin(3θ) = 3sin(θ) - 4sin^3(θ)

Now, let's calculate the values step by step:

sin(π/10) * sin(3π/10) * cos(π/3) = sin(π/10) * sin(3π/10) * (1/2) * √3 (Using the identity sin(π/3) = √3/2)

Now, we need to find the values of sin(π/10) and sin(3π/10). We can use the identity sin(3θ) = 3sin(θ) - 4sin^3(θ) to find sin(3π/10) in terms of sin(π/10):

sin(3π/10) = 3sin(π/10) - 4sin^3(π/10)

Now, substitute this into the expression:

(sin(π/10)) * (3sin(π/10) - 4sin^3(π/10)) * (1/2) * √3

Now, let's simplify further:

(3/2) * sin^2(π/10) * (1 - 4sin^2(π/10)) * √3

Now, you can calculate sin(π/10) and simplify the expression:

sin(π/10) ≈ 0.3090169943749474 (approximately)

Now, plug this value into the expression:

(3/2) * (0.3090169943749474)^2 * (1 - 4(0.3090169943749474)^2) * √3

Now, calculate the numerical value:

≈ 0.239285957 (rounded to 9 decimal places)

So, sin(π/10) * sin(3π/10) * cos(π/3) is approximately 0.239285957.