Question

Cos альфа= 1/4 найти sin tg ctg​

Answer 1

Ответ:

Объяснение:на фото

Answer 2

To find the values of sin, tan, and cot for a given angle α, we first need to determine the value of sin(α), then use that to calculate tan(α) and cot(α).

Given that cos(α) = 1/4, we can use the Pythagorean identity to find sin(α):

sin^2(α) + cos^2(α) = 1

sin^2(α) + (1/4)^2 = 1

sin^2(α) + 1/16 = 1

sin^2(α) = 1 - 1/16

sin^2(α) = 15/16

Now, taking the square root of both sides:

sin(α) = ±√(15/16)

Since the sine function is positive in the first and second quadrants, we take the positive value:

sin(α) = √(15/16)

Now, we can calculate tan(α) and cot(α):

tan(α) = sin(α) / cos(α)

cot(α) = cos(α) / sin(α)

tan(α) = √(15/16) / (1/4) = (4/4) * √(15/16) = √(15/16) = √15 / 4

cot(α) = (1/4) / √(15/16) = (1/4) / (√15 / 4) = 1 / √15 = √15 / 15

So, the values are:

sin(α) = √(15/16) tan(α) = √15 / 4 cot(α) = √15 / 15