Question

Найдите sin t , если cos t = - 8 17 ,π

Answer 1

To find sin(t), we can use the Pythagorean trigonometric identity, which states that for any angle t in a right-angled triangle:

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

Given that cos(t) = -8/17, we can calculate sin(t) as follows:

sin^2(t) + (-8/17)^2 = 1 sin^2(t) + 64/289 = 1 sin^2(t) = 1 - 64/289 sin^2(t) = (289 - 64)/289 sin^2(t) = 225/289

Now, to find sin(t), we take the square root of both sides (remembering that sin(t) is positive in this case because t is in the second quadrant, where sine is positive):

sin(t) = sqrt(225/289) sin(t) = 15/17

So, sin(t) = 15/17.