Question

Если cos = -4/5 (дробь) и /2 < < , то sin = а) 3/5b) -3/5c) +- 3/5d) 4/5

Answer 1

Ответ:

а) 3/5

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Answer 2

To solve this problem, we'll use the Pythagorean identity and the given information about cos(θ).

The Pythagorean identity states: sin^2(θ) + cos^2(θ) = 1

Given: cos(θ) = -4/5

Now, we can find sin(θ):

sin^2(θ) + cos^2(θ) = 1

sin^2(θ) + (-4/5)^2 = 1

sin^2(θ) + 16/25 = 1

sin^2(θ) = 1 - 16/25

sin^2(θ) = (25 - 16) / 25

sin^2(θ) = 9 / 25

Taking the square root of both sides:

sin(θ) = ±√(9/25)

sin(θ) = ±(3/5)

Since we know that 0 < θ < π/2 (0 to 90 degrees) and cos(θ) is negative, we can conclude that sin(θ) must also be negative in this range.

Therefore, sin(θ) = -3/5.

The correct answer is (b) -3/5.