Question

Найдите cosα, если sinα=7:25 и α∈(0 ; π:2).

Answer 1

Cos^2α+ sin^2α=1

Тогда: cosα = √(1 – 49/625)

cosα = 24/25

И cosα принадлежит I четверти

Answer 2

To find the value of cos(α), we can use the trigonometric identity:

sin²(α) + cos²(α) = 1

Given that sin(α) = 7/25, we can use this information to find cos(α).

sin²(α) = (7/25)² = 49/625

Now, we can rearrange the identity to solve for cos²(α):

cos²(α) = 1 - sin²(α) = 1 - 49/625 = 576/625

Finally, taking the square root of cos²(α) gives us the value of cos(α):

cos(α) = √(576/625) = ±24/25

Since α is in the range (0, π/2), cos(α) is positive. Thus, the value of cos(α) is:

cos(α) = 24/25