Question

Sin a, tg a и ctg a, если cos a​

Answer 1

1) Находим sin a, по тригонометрическому торжеству

sin²a + cos²a = 1

Получается

sin²a = 1 - cos²a

(для простоты запиши все это под корнем, просто я не знаю, как это с телефона показать)

2) Т.к мы знаем и sin a и cos a, легко найдём tg и ctg

tg a = sin a ÷ cos a

ctg a = cos a ÷ sin a

Всё поставляешь и считаешь

Answer 2

To find the values of sin(a), tan(a), and cot(a) given cos(a), we can use trigonometric identities. The Pythagorean identity is especially helpful in this case:

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

We can solve for sin(a) by rearranging the equation:

sin^2(a) = 1 - cos^2(a) sin(a) = √(1 - cos^2(a))

Now, let's find the values of sin(a), tan(a), and cot(a) given the value of cos(a).

1. sin(a) = √(1 - cos^2(a))
2. tan(a) = sin(a) / cos(a)
3. cot(a) = 1 / tan(a)

Substituting the given value of cos(a) into the equations:

1. sin(a) = √(1 - cos^2(a))
2. tan(a) = sin(a) / cos(a)
3. cot(a) = 1 / tan(a)

Therefore, if you provide the value of cos(a), I can calculate sin(a), tan(a), and cot(a) for you.