How can I find the maximum value of $ f(t)=x*cos(t)+sin(t)*(wy*z-wz*y)+wx*(wx*x+wy*y+wz*z)*(1-cos(t))$;

Question

I have the function:

$f(t)=x* cos(t)+sin(t)*(wy * z-wz* y)+wx*(wx* x+wy* y+wz* z)*(1-cos(t)).$

Only $t$ is variable ($t$ is positive real number).

$x,y,z,wx,wy,wz$ are constants real numbers. and $wx^2+wy^2+wz^2=1$;

Answer 1

Hint:

$a\sin t+b\cos t=\sqrt{a^2+b^2}\sin(t+\alpha)$ for some $\alpha\in[0,2\pi)$. It's maximum value is $\sqrt{a^2+b^2}$.