Question

Cos a = -5/13, п< a< 3п/2 найти sin a

Answer 1

У меня вот че поулчилось

Answer 2

To find the value of sin(a), we can use the Pythagorean trigonometric identity:

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

Since we already know the value of cos(a) as -5/13, we can plug it into the equation:

sin^2(a) + (-5/13)^2 = 1

Now, solve for sin(a):

sin^2(a) + 25/169 = 1

sin^2(a) = 1 - 25/169

sin^2(a) = (169 - 25) / 169

sin^2(a) = 144 / 169

Now, take the square root of both sides:

sin(a) = ±√(144 / 169)

Since we know that "a" is in the second quadrant (π/2 < a < 3π/2) and the cosine is negative, we can determine that the sine is positive.

sin(a) = √(144 / 169)

sin(a) = √144 / √169

sin(a) = 12 / 13

So, the value of sin(a) is 12/13.