Question

Найти sin x, если cos x = - 1/3

Answer 1

Ответ:

2√2/3

Пошаговое объяснение:

cos x = - 1/3

sin²x+cos²x=1

sinx= √1-cos²x= √1-(-1/3)²=√9/9-1/9=√8/9=2√2/3

Answer 2

Sin^2(x) + cos^2(x) = 1
sin^2(x) = 1 - cos^2(x)
sin^2(x) = 1 - (-1/3)^2
sin^2(x) = 1 - 1/9
sin^2(x) = 8/9
sin(x) = (2*корень из 2)/3

Answer 3

To find sin(x) given that cos(x) = -1/3, we can use the Pythagorean identity, which states:

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

We already know cos(x) = -1/3, so we can substitute this value into the equation:

sin^2(x) + (-1/3)^2 = 1

sin^2(x) + 1/9 = 1

Now, we can isolate sin^2(x):

sin^2(x) = 1 - 1/9

sin^2(x) = 9/9 - 1/9

sin^2(x) = 8/9

Now, we take the square root of both sides to find sin(x):

sin(x) = ±√(8/9)

Since sin(x) can be positive or negative, we have two possible solutions:

1. sin(x) = √(8/9) = √(8)/√(9) = √(8)/3 ≈ 0.942809

2. sin(x) = -√(8/9) = -√(8)/√(9) = -√(8)/3 ≈ -0.942809

So, the two possible values for sin(x) when cos(x) = -1/3 are approximately 0.942809 and -0.942809.