Question

Найти ctgA если sinA=√5/5

Answer 1

..........)))))))))))))))))))))))).....

Answer 2

To find the value of cotangent (ctg) of angle A, we can use the relationship between sine and cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle.

The tangent of angle A can be found using the given information. We know that the sine of angle A is equal to √5/5. The tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle.

We can start by finding the cosine of angle A using the Pythagorean identity: sin^2(A) + cos^2(A) = 1. Since we know sin(A) = √5/5, we can substitute it into the equation and solve for cos(A):

(√5/5)^2 + cos^2(A) = 1 5/25 + cos^2(A) = 1 1/5 + cos^2(A) = 1 cos^2(A) = 1 - 1/5 cos^2(A) = 4/5

Taking the square root of both sides, we get:

cos(A) = ±√(4/5)

Since sine is positive (√5/5), cosine should also be positive to maintain the positive values of the trigonometric ratios in the first quadrant.

cos(A) = √(4/5)

Now, we can use the tangent definition to find the tangent of angle A:

tan(A) = sin(A) / cos(A) tan(A) = (√5/5) / (√(4/5))

Simplifying the expression, we get:

tan(A) = (√5/5) / (√4/√5) tan(A) = (√5/5) * (√5/√4) tan(A) = (√5 * √5) / (5 * √4) tan(A) = 5 / (5 * 2) tan(A) = 1/2

Finally, we can find the cotangent of angle A by taking the reciprocal of the tangent:

ctg(A) = 1 / tan(A) ctg(A) = 1 / (1/2) ctg(A) = 2

Therefore, ctg(A) is equal to 2.