Question

Найдите sin a и tg a ,если cos A = √15/4

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

To find sin(a) and tan(a) given that cos(A) = √15/4, we can use the trigonometric identity:

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

First, let's find sin(A):

sin^2(A) = 1 - cos^2(A) sin^2(A) = 1 - (√15/4)^2 sin^2(A) = 1 - 15/16 sin^2(A) = (16 - 15)/16 sin^2(A) = 1/16

Taking the square root of both sides:

sin(A) = ±1/4

Since A is not specified, we cannot determine the sign of sin(A) with the given information. Therefore, sin(A) can be either +1/4 or -1/4.

Now, let's find tan(A):

tan(A) = sin(A) / cos(A)

If sin(A) = +1/4:

tan(A) = (1/4) / (√15/4) tan(A) = 1 / √15

If sin(A) = -1/4:

tan(A) = (-1/4) / (√15/4) tan(A) = -1 / √15

So, the values of tan(A) are 1/√15 or -1/√15, depending on the sign of sin(A).