Question

Найти sin a и cos a,если ctg =-8/15

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To find the values of sin(a) and cos(a) when cotangent (ctg) is equal to -8/15, we can use the following trigonometric identities:

1. cot(a) = 1 / tan(a)
2. cot(a) = cos(a) / sin(a)

First, we can find the values of sin(a) and cos(a) using the given cot(a) = -8/15:

cot(a) = -8/15

Now, let's use the first identity to find the value of tan(a):

tan(a) = 1 / cot(a) = 1 / (-8/15) = -15/8

Next, we can use the second identity to find the values of sin(a) and cos(a):

cot(a) = cos(a) / sin(a)

Since we have tan(a) = -15/8, and tan(a) = sin(a) / cos(a), we can equate these:

-15/8 = sin(a) / cos(a)

Now, we can solve for sin(a) and cos(a). Let's assume sin(a) = k, then:

-15/8 = k / cos(a)

Now, solve for cos(a):

cos(a) = k / (-15/8) = -8k/15

Since sin(a)^2 + cos(a)^2 = 1, we can substitute the values of sin(a) and cos(a) into this equation:

k^2 + (-8k/15)^2 = 1

Solving for k:

k^2 + 64k^2/225 = 1

(225k^2 + 64k^2) / 225 = 1

289k^2 = 225

k^2 = 225 / 289

k^2 = 25 / 289

k = ±√(25/289)

k = ±5/17

Now, we have two possible solutions for sin(a):

1. sin(a) = 5/17
2. sin(a) = -5/17

Finally, we can find the corresponding values of cos(a) using cos(a) = -8k/15:

1. cos(a) = -8 * (5/17) / 15 = -40/255 = -8/51
2. cos(a) = -8 * (-5/17) / 15 = 40/255 = 8/51

So, the solutions for sin(a) and cos(a) when cot(a) = -8/15 are:

1. sin(a) = 5/17, cos(a) = -8/51
2. sin(a) = -5/17, cos(a) = 8/51