Question

Cosx, если sinx=-15/17 π

Answer 1

Cos^2 x+sin^2 x  =  1
cos x  =  корень (1-sin^2 x)
cos x  =  корень (1-(-15/17))  =  корень (1  15/17)

Answer 2

If sin(x) = -15/17π, we can use the Pythagorean trigonometric identity to find the value of cos(x).

The Pythagorean identity is given by:

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

Since sin(x) = -15/17π, we can square it:

sin^2(x) = (-15/17π)^2 sin^2(x) = 225/289π^2

Now, let's plug this value into the Pythagorean identity:

(225/289π^2) + cos^2(x) = 1

Next, solve for cos^2(x):

cos^2(x) = 1 - 225/289π^2 cos^2(x) = (289 - 225)/(289π^2) cos^2(x) = 64/(289π^2)

Now, find cos(x) by taking the square root of both sides:

cos(x) = ±√(64/(289π^2))

Since the cosine function is positive in the first and fourth quadrants, we take the positive square root:

cos(x) = √(64/(289π^2))

Finally, simplify the expression:

cos(x) = 8/(17π)

So, cos(x) = 8/(17π) when sin(x) = -15/17π.