# Thread: Prove that maximum of sin^2(x)+sin^2(y)+sin^2(z) with x+y+z=180 is when x=y=z=60

1. ## Prove that maximum of sin^2(x)+sin^2(y)+sin^2(z) with x+y+z=180 is when x=y=z=60

Prove that maximum of $sin^2(x)+sin^2(y)+sin^2(z)$ with $x+y+z=180$ is when $x=y=z=60$

2. Originally Posted by oleholeh
Prove that maximum of $sin^2(x)+sin^2(y)+sin^2(z)$ with $x+y+z=180$ is when $x=y=z=60$
This is a function from R^3 -> R. Find the Jacobian, (a 1x3 matrix, gradient). See if (x,y,z) = (60,60,60) is a critical point. then find the Hessian (the matrix of second order partial derivatives.), then use the second partial derivative test.