Question

Найдите cosα, если sinα = √21/5 и ​

Answer 1

Відповідь: -0,4 Решение задания приложено

Answer 2

cosα = -√(1 - sin²α) = -√(1 - 21/25) = -√((25 - 21)/25) = -√(4/25) = -2/5

Answer 3

To find cos(α) given that sin(α) = √21/5, we can use the Pythagorean identity for trigonometric functions:

sin^2(α) + cos^2(α) = 1

Since we already know sin(α) = √21/5, we can substitute it into the equation:

(√21/5)^2 + cos^2(α) = 1

Solving for cos(α):

(21/25) + cos^2(α) = 1

cos^2(α) = 1 - 21/25

cos^2(α) = 25/25 - 21/25

cos^2(α) = 4/25

Taking the square root of both sides to find cos(α):

cos(α) = ±√(4/25)

cos(α) = ±(2/5)

Since the cosine function has both positive and negative values, we have two possible solutions for cos(α):

1. cos(α) = 2/5
2. cos(α) = -2/5

Without further information about the quadrant in which α lies, we cannot determine the exact value of cos(α). However, we know that it can be either 2/5 or -2/5.