Question

Sinx=5/13 x Є (π/2; π) cosx - ?

Answer 1

Ответ:

cosx=-12/13, т.к. угол второй четверти

Объяснение:

решение через тригонометрическую единицу

Answer 2

To find the value of cos(x) given sin(x) = 5/13 and x belongs to the interval (π/2, π), we can use the Pythagorean identity.

The Pythagorean identity states that sin^2(x) + cos^2(x) = 1.

Since we know sin(x) = 5/13, we can substitute this value into the equation:

(5/13)^2 + cos^2(x) = 1

Simplifying the equation:

25/169 + cos^2(x) = 1

Subtracting 25/169 from both sides:

cos^2(x) = 1 - 25/169

cos^2(x) = 144/169

Taking the square root of both sides:

cos(x) = ± √(144/169)

cos(x) = ± (12/13)

Since x belongs to the interval (π/2, π), which is the second quadrant, the cosine value should be negative.

Therefore, cos(x) = -12/13.