Question

Найдите значение ctg α, если sinα=2/​√​13​​​​​​​ и 90 ∘<α<180

Answer 1

cos второй четверти отрицательный

cos α= - √(1-(2/√13²)) = - √9/13= - 3/√13

ctgα = cosα/sinα = -3/√13 : 2/√13 =  -3/√13 * √13 /2 = -3/2  = -1,5

Answer 2

To find the value of cotangent (ctg) α, we first need to determine the value of cosine (cos) α, as cotangent is the reciprocal of tangent and tangent is the ratio of sine to cosine. We can use the Pythagorean identity to find cos α:

sin² α + cos² α = 1

Given that sin α = 2/√13, we can substitute it into the equation:

(2/√13)² + cos² α = 1

Solving for cos α:

(4/13) + cos² α = 1 cos² α = 1 - 4/13 cos² α = 9/13

Now, since 90° < α < 180°, we know that α is in the second quadrant where cosine is negative. Therefore, cos α = -√(9/13) = -3/√13.

Finally, we can find cot α (ctg α) as the reciprocal of tangent:

cot α = 1 / tan α cot α = 1 / (sin α / cos α) cot α = cos α / sin α

cot α = (-3/√13) / (2/√13)

cot α = -3/2

So, the value of ctg α (cotangent of α) is -3/2.