Question

Sin 2х,если sin x=1/3,x- из 2 четверти​

Answer 1

Ответ:

решение на фотографии

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Answer 2

To find the value of sin(2x) given that sin(x) = 1/3 and x is in the second quadrant, we can use the double angle formula for sine.

The double angle formula for sine states that sin(2x) = 2*sin(x)*cos(x).

Since sin(x) = 1/3, we can determine the value of cos(x) using the Pythagorean identity: sin^2(x) + cos^2(x) = 1.

Plugging in the value of sin(x) = 1/3, we have:

(1/3)^2 + cos^2(x) = 1 1/9 + cos^2(x) = 1 cos^2(x) = 1 - 1/9 cos^2(x) = 8/9 cos(x) = sqrt(8/9) cos(x) = sqrt(8)/3

Now we can substitute these values into the double angle formula:

sin(2x) = 2sin(x)cos(x) sin(2x) = 2(1/3)(sqrt(8)/3) sin(2x) = 2sqrt(8)/9

Therefore, sin(2x) = 2sqrt(8)/9 when sin(x) = 1/3 and x is in the second quadrant.