Question

Вычислить cos (α), если sin (α)=0,8 и α ∈ [0;π/2]

Answer 1

Ответ:

0,6

Пошаговое объяснение:

α ∈ [0;π/2] - cos имеет знак "+"

$cos\alpha =\sqrt{1-sin^\alpha } =\sqrt{1-0,8^2}=\sqrt{1-0,64} =\sqrt{0,36} =0,6$

Answer 2

Ответ: cos α=√(1-sin²α)=√(1-0,8²)=0,6 c учётом заданного диапазона углов.

Пошаговое объяснение:

Answer 3

To calculate cos(α) given sin(α) = 0.8 and α ∈ [0, π/2], you can use the Pythagorean trigonometric identity:

sin^2(α) + cos^2(α) = 1

Since sin(α) = 0.8, we can square it and solve for cos(α):

0.8^2 + cos^2(α) = 1

0.64 + cos^2(α) = 1

cos^2(α) = 1 - 0.64

cos^2(α) = 0.36

Taking the square root of both sides:

cos(α) = ±√(0.36)

However, we need to determine whether cos(α) is positive or negative in the given range [0, π/2]. Since α is in the first quadrant (0 to π/2), cos(α) is positive. Thus,

cos(α) = √(0.36) ≈ 0.6

So, cos(α) is approximately 0.6.