Question

Найдите cos l; tg l, если sin l=4/5

Answer 1

Ответ:

Объяснение:

1=cos^2 l + sin^2 l

Cos^2 l = 1- sin^2 l

Cos^2 l = 1- 4/5 = 1/5

Cos l = корень из 1/5 = 1/корень из 5

Tg l = sin l / Cos l

Tg l = 4/5 : 1/корень из 5 = 4корень из 5 / 5

Answer 2

To find cos(l) and tan(l) given sin(l) = 4/5, we can use the Pythagorean trigonometric identity, which states:

sin^2(l) + cos^2(l) = 1

We know that sin(l) = 4/5, so we can square this value:

sin^2(l) = (4/5)^2 = 16/25

Now, we can use the Pythagorean identity to find cos(l):

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

Taking the square root of both sides:

cos(l) = ±√(9/25) = ±(3/5)

Since sine is positive in the first and second quadrants, we know that cos(l) must be positive as well. So we take the positive value:

cos(l) = 3/5

Now, we can find tan(l) using the identity:

tan(l) = sin(l) / cos(l) = (4/5) / (3/5) = (4/5) * (5/3) = 4/3

Therefore, cos(l) = 3/5 and tan(l) = 4/3.