Question

Sin альфа=-4/5. Найдите 25cos2альф

Answer 1

1)cos2x = cos²x - sin²x
cos²x = 1 - sin²x
cos²x = 1 - 16/25cos²x = 9/25
2)cos2x = 9/25 - 16/25
cos2x = -7/25

Answer 2

Cos2x=cosx^2-sinx^2=1-2*sinx^2=  1-32/25= -7/25
25cos2x= -7

Answer 3

To find the value of 25cos^2(α) when sin(α) = -4/5, we can use the Pythagorean trigonometric identity:

sin^2(α) + cos^2(α) = 1

Since we know that sin(α) = -4/5, we can square it to get sin^2(α):

sin^2(α) = (-4/5)^2 = 16/25

Now, we can rearrange the Pythagorean identity to solve for cos^2(α):

cos^2(α) = 1 - sin^2(α) cos^2(α) = 1 - 16/25 cos^2(α) = (25 - 16)/25 cos^2(α) = 9/25

Finally, to find 25cos^2(α):

25cos^2(α) = 25 * (9/25) = 9

So, 25cos^2(α) = 9.