Question

Sinx =4\5 90°<альфа <180° cosa​

Answer 1

Ответ:

cos a=корень из 1-16/25=-3/5

Answer 2

To find the value of cos(α) given that sin(α) = 4/5 and α is in the range 90° < α < 180°, you can use the Pythagorean identity for trigonometric functions. The Pythagorean identity is:

sin²(α) + cos²(α) = 1

Given that sin(α) = 4/5, you can square this value and then solve for cos(α):

(sin(α))² + cos(α)² = 1

(4/5)² + cos(α)² = 1

(16/25) + cos(α)² = 1

Now, subtract 16/25 from both sides to isolate cos(α)²:

cos(α)² = 1 - 16/25

cos(α)² = 25/25 - 16/25

cos(α)² = 9/25

Now, take the square root of both sides to find cos(α):

cos(α) = ±√(9/25)

cos(α) = ±(3/5)

Since α is in the range 90° < α < 180°, which is in the second quadrant, cos(α) is negative. So, the value of cos(α) is -3/5.