Question

Найдите cos , если sin =√7/4 и ∈ (0; /2) .

Answer 1

0,75. Решение задания приложено

Answer 2

To find the value of cos given that sin = √7/4 and θ is in the interval (0, π/2), we can use the Pythagorean identity:

cos^2 θ + sin^2 θ = 1

Substituting the given value of sin, we have:

cos^2 θ + (√7/4)^2 = 1 cos^2 θ + 7/16 = 1 cos^2 θ = 1 - 7/16 cos^2 θ = 16/16 - 7/16 cos^2 θ = 9/16

Taking the square root of both sides:

cos θ = ±√(9/16)

Since θ is in the interval (0, π/2), we can conclude that cos θ is positive. Therefore:

cos θ = √(9/16) cos θ = 3/4