Cos
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– cos(θ)=cos(-θ) – sin(-θ)=-sin(θ) – cos(π/2-θ)=sin(θ) – sin(π/2-θ)= cos(θ) – cos(π/2+θ)=-sin(θ) – sin(π/2+θ)= cos(θ) – cos(π-θ)=-cos(θ) – sin(π-θ)= sin(θ) – cos(π+θ)=-cos(θ) – sin(π+θ)=-sin(θ) – cos 2 (θ)=(1/2)*[1+cos(2θ)] – sin 2 (θ)=(1/2)*[1-cos(2θ)] – sin(2θ)=cos(θ)*sin(θ) – cosθ=1/2 * {exp(jθ)+exp(-jθ)} à Ταυτότητα Euler – sinθ=(1/2j) * {exp(jθ)-exp(-jθ)} à Ταυτότητα Euler – exp(±jθ)= cosθ ± j*sinθ à Ταυτότητα Euler
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cos
Transcript of Cos
cos()=cos(-) sin(-)=-sin() cos(/2-)=sin() sin(/2-)= cos() cos(/2+)=-sin() sin(/2+)= cos() cos(-)=-cos() sin(-)= sin() cos(+)=-cos() sin(+)=-sin() cos2()=(1/2)*[1+cos(2)] sin2()=(1/2)*[1-cos(2)] sin(2)=cos()*sin() cos=1/2 * {exp(j)+exp(-j)} Euler sin=(1/2j) * {exp(j)-exp(-j)} Euler exp(j)= cos j*sin Euler
