Question

Ctg a=-8/15, cos a-?

Answer 1

Ваше решение готово:
tg = 1/ctg => tg = 15/8

Найдем cos a: 1 + tg^2 a = 1/cos^2 a
1 + (15/8)^2 = 1/cos^2 a
1/cos^2 a = 1 + 225/64
1/cos^2 a = 289/64
cos^2 a = 64/289
cos a1 = 8/17, cos a2 = -8/17, но так как cos в первой четверти положителен, то выбираем значение cos a = 8/17
надеюсь  вам помогла)

Answer 2

To find the value of cosine (cos) of angle a when the tangent (ctg) of a is given, we can use the identity relating tangent and cosine:

ctg(a) = 1 / tan(a)

However, keep in mind that ctg is not a widely used abbreviation. The more common abbreviation for the cotangent function is cot. I'll proceed with cot(a) to avoid any confusion.

The identity we'll use is:

cot(a) = 1 / tan(a)

Given cot(a) = -8/15, we can find tan(a) as follows:

cot(a) = 1 / tan(a)

-8/15 = 1 / tan(a)

Now, let's solve for tan(a):

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

To divide by a fraction, we can multiply by its reciprocal:

tan(a) = -15/8

Now, we can use the Pythagorean identity to find the cosine of a:

tan(a) = sin(a) / cos(a)

The Pythagorean identity is:

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

Since we already have tan(a) = -15/8, we can use the fact that tan(a) = sin(a) / cos(a) to find sin(a):

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

Next, we'll use the Pythagorean identity to find cos(a):

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

Substitute sin(a) = -15/8:

(-15/8)^2 + cos^2(a) = 1

Simplify and solve for cos(a):

225/64 + cos^2(a) = 1

cos^2(a) = 1 - 225/64

cos^2(a) = (64 - 225) / 64

cos^2(a) = -161/64

Since cosine is positive in the first and fourth quadrants, we take the positive square root:

cos(a) = sqrt(-161/64)

However, we encounter an issue here. The expression under the square root is negative, which means there is no real solution for cos(a) in this case.

So, for the given value of cot(a) = -8/15, the cosine cos(a) is undefined in the real number system.