Question

Cos20°sin100°sin(-50°)ctg200°

Answer 1

Вот правильный ответ)

Answer 2

To simplify the expression:

1. Convert the trigonometric functions to their respective values using known trigonometric identities or values from a unit circle.
2. Calculate the result.

Let's break it down step by step:

• cos(20°) is equal to cos(180° - 160°), and since cos(180° - θ) = -cos(θ), we have cos(20°) = -cos(160°).
• sin(100°) is equal to sin(180° - 80°), and since sin(180° - θ) = sin(θ), we have sin(100°) = sin(80°).
• sin(-50°) is equal to -sin(50°) because the sine function is an odd function.
• cot(200°) is equal to 1/tan(200°).

Now, let's calculate these values:

1. cos(160°) is approximately -0.9397 (you can use a calculator or trigonometric tables for this).
2. sin(80°) is approximately 0.9848.
3. -sin(50°) is approximately -0.7660.
4. cot(200°) is equal to 1/tan(200°). tan(200°) is approximately -1.3764, so cot(200°) is approximately -1/(-1.3764), which is approximately 0.7266.

Now, multiply these values together:

-0.9397 * 0.9848 * (-0.7660) * 0.7266 ≈ 0.5463

So, the value of the expression is approximately 0.5463.