Question

Найдите sinx, если cosx=3 корень из 11 разделить на 10

Answer 1

Косинус положителен в I и IV четвертях, а синус в I четверти положителен и во IV четверти отрицателен. Из основного тригонометрического тождества, найдем sin x:

$\tt \sin x=\pm\sqrt{1-\cos^2x} =\pm\sqrt{1-\bigg(\dfrac{3\sqrt{11}}{10}\bigg)^2} =\pm\sqrt{\dfrac{100-99}{100}} =\pm\dfrac{1}{10}$

Answer 2

To find the value of sin(x) when cos(x) = (3√11) / 10, we can use the Pythagorean trigonometric identity:

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

Since we know the value of cos(x), we can find sin(x) as follows:

sin^2(x) + (3√11 / 10)^2 = 1 sin^2(x) + (9 * 11 / 100) = 1 sin^2(x) + 99 / 100 = 1 sin^2(x) = 1 - 99 / 100 sin^2(x) = 1/100

Now, taking the square root of both sides:

sin(x) = ± √(1/100)

Since sine is positive in the first and second quadrants (0 ≤ x ≤ π), we take the positive value:

sin(x) = √(1/100) = 1/10

So, sin(x) = 1/10.