Question

Sin α=0.2756 (треба знайти кут) tg α=0.5498 cos β=0.6691 tg β=2.0965 help)

Answer 1

sin α=0.2756; ∠α=16°

tg α=0.5498; ∠α=28,5°

cos β=0.6691; ∠β=48°

tg β=2.0965; ∠β=64,5°

(використано таблиці синусів, косинусов і тангенсів кутів)

Answer 2

sin α=0.2756; α=16°

tg α=0.5498; α=28,8°

cos β=0.6691;β=48°

tg β=2.0965; β=64,5°

Answer 3

To find the angle α and β, we can use trigonometric identities and equations. Let's solve each equation step by step:

1. Sin α = 0.2756 To find α, we can use the inverse sine function (sin⁻¹) on both sides of the equation: α = sin⁻¹(0.2756) Using a calculator, the approximate value of α is α ≈ 16.23 degrees.

2. tg α = 0.5498 To find α, we can use the inverse tangent function (tan⁻¹) on both sides of the equation: α = tan⁻¹(0.5498) Using a calculator, the approximate value of α is α ≈ 29.91 degrees.

3. cos β = 0.6691 To find β, we can use the inverse cosine function (cos⁻¹) on both sides of the equation: β = cos⁻¹(0.6691) Using a calculator, the approximate value of β is β ≈ 47.89 degrees.

4. tg β = 2.0965 To find β, we can use the inverse tangent function (tan⁻¹) on both sides of the equation: β = tan⁻¹(2.0965) Using a calculator, the approximate value of β is β ≈ 63.49 degrees.

Therefore, the values of the angles are approximately: α ≈ 16.23 degrees β ≈ 47.89 degrees