Question

Даю 30 баллов cos 765 - sin 750 - cos 1035 и sin 11П / 3 + cos 690 - cos 19П / 3

Answer 1

Ответ:

0,5

-0,5

Объяснение:

cos 765 - sin 750 - cos 1035 = cos(2*360+45) - sin(2*360+30)-cos(3*360-45)=

= cos45 - sin30 - cos(-45)=cos45 - sin30 - cos45=sin30=0,5

sin(11π/3) + cos690 - cos(19π/3)=sin(2*2π - π/3) + cos(2*360 - 30) - cos(3*2π + π/3)= sin(- π/3) + cos(-30) - cosπ/3= -sinπ/3 + cos30 - cosπ/3= -√2/3 + √2/3 -0,5=-0,5

Answer 2

To calculate the given expression, we need to use trigonometric identities and calculate the values of cosines and sines. Keep in mind that "П" is the Greek letter Pi (approximately equal to 3.14159).

Let's break it down step by step:

1. Convert angles from degrees to radians: cos(765°) = cos(765 * π / 180) sin(750°) = sin(750 * π / 180) cos(1035°) = cos(1035 * π / 180) sin(11П / 3) = sin(11 * π / 3)

2. Use trigonometric identities: cos(θ) = cos(θ + 2πn), where n is an integer sin(θ) = sin(θ + 2πn), where n is an integer

Now, let's calculate each part of the expression:

cos(765°) = cos(765 * π / 180) ≈ cos(13.343 * π) ≈ cos(0.343 * π) ≈ cos(0.343 * 3.14159) ≈ cos(1.0781) ≈ 0.4688

sin(750°) = sin(750 * π / 180) ≈ sin(13.089 * π) ≈ sin(0.089 * π) ≈ sin(0.089 * 3.14159) ≈ sin(0.2797) ≈ 0.2769

cos(1035°) = cos(1035 * π / 180) ≈ cos(18.052 * π) ≈ cos(0.052 * π) ≈ cos(0.052 * 3.14159) ≈ cos(0.1637) ≈ 0.9871

sin(11П / 3) = sin(11 * π / 3) ≈ sin(3.666 * π) ≈ sin(0.666 * π) ≈ sin(0.666 * 3.14159) ≈ sin(2.089) ≈ 0.8865

cos(690°) = cos(690 * π / 180) ≈ cos(12.042 * π) ≈ cos(0.042 * π) ≈ cos(0.042 * 3.14159) ≈ cos(0.132) ≈ 0.9907

cos(19П / 3) = cos(19 * π / 3) ≈ cos(6.333 * π) ≈ cos(0.333 * π) ≈ cos(0.333 * 3.14159) ≈ cos(1.0472) ≈ 0.5000

Now, let's plug in these values into the original expression:

30 * (cos(765) - sin(750) - cos(1035) + sin(11П / 3) + cos(690) - cos(19П / 3))

30 * (0.4688 - 0.2769 - 0.9871 + 0.8865 + 0.9907 - 0.5000)

30 * (0.572) ≈ 17.16

So, the result of the given expression is approximately 17.16.