Question

Найдите tg если cos a = - 1 /корень из 2 и a принадлежит (0,5п ;п)

Answer 1

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Answer 2

Finding the Value of tg(a) Given cos(a) = -1/√2 and a ∈ (0.5π, π)

To find the value of tg(a) given that cos(a) = -1/√2 and a belongs to the interval (0.5π, π), we can use the trigonometric identity:

tg(a) = sin(a) / cos(a)

Since we know the value of cos(a), we can substitute it into the equation:

tg(a) = sin(a) / (-1/√2)

To find the value of sin(a), we can use the Pythagorean identity:

sin²(a) + cos²(a) = 1

Substituting the value of cos(a) = -1/√2, we can solve for sin(a):

sin²(a) + (-1/√2)² = 1

sin²(a) + 1/2 = 1

sin²(a) = 1 - 1/2

sin²(a) = 1/2

Taking the square root of both sides, we get:

sin(a) = ±√(1/2)

Since a belongs to the interval (0.5π, π), sin(a) is positive. Therefore:

sin(a) = √(1/2) = 1/√2

Substituting the values of sin(a) and cos(a) into the equation for tg(a), we get:

tg(a) = (1/√2) / (-1/√2)

Simplifying the expression, we have:

tg(a) = -1

Therefore, the value of tg(a) when cos(a) = -1/√2 and a belongs to the interval (0.5π, π) is -1.