Question

What and how to get the roots (zeros) for the following function:
-sin(2x)+cos(x)

Answer 1

x=0.5π+kπ, k∈Z v x=1/6π+2kπ, k∈Z v x=5/6π+2kπ, k∈Z

Explanation:

f(x)=-sin2x+cosx

f(x)=0 , sin2x=2sinxcosx

-sin2x+cosx=0

-2sinxcosx+cosx=0

cosx(-2sinx+1)=0

cosx=0 v -2sinx+1=0

cosx=0 v sinx=0.5

cosx=0 when x=0.5π+kπ, k∈Z On the graph of cosx, the value of 0 repeats cyclically by π. The rest value repeat cyclically by 2π.

sinx=0.5 x=1/6π+2kπ, k∈Z v x=5/6π+2kπ, k∈Z On the graph sinx, the value of 0.5 for x=1/6π (1st quater) and x=5/6π (2nd quater) repeats cyclically by 2π.

x=0.5π+kπ, k∈Z v x=1/6π+2kπ, k∈Z v x=5/6π+2kπ, k∈Z