Question

设f( θ)=2cos^3θ + sin^2 (2π-θ)+cos(-θ)-3 / 2+2cos^2(π+θ) + co

Answer 1

f( θ)=2cos^3θ + sin^2 (2π-θ)+cos(-θ)-3 / 2+2cos^2(π+θ) + cos(2π-θ)

=2cos^3θ + sin^2 θ+cosθ-3 / 2+2cos^2θ + cosθ

=2cos^3θ+ cos^2θ +2cosθ+(sin^2 θ+cos^2θ )-3/ 2

=2cos^3θ+ cos^2θ +2cosθ-1/ 2

∵cosπ/3=1/2

f(π/3) =2(1/2)^3+ (1/2)^2 +2(1/2)-1/ 2

=1/4+1/4+1-1/2

=1