Công thức cung liên kết

Cung đối
\(\cos(-\alpha)=\cos\alpha\)
\(\sin(-\alpha)=-\sin\alpha\)
\(\tan(-\alpha)=-\tan\alpha\)
\(\cot(-\alpha)=-\cot\alpha\)

Cung bù
\(\sin(\pi-\alpha)=\sin\alpha\)
\(\cos(\pi-\alpha)=-\cos\alpha\)
\(\tan(\pi-\alpha)=-\tan\alpha\)
\(\cot(\pi-\alpha)=-\cot\alpha\)

Cung hơn kém \(\pi\)
\(\sin(\pi+\alpha)=-\sin\alpha\)
\(\cos(\pi+\alpha)=-\cos\alpha\)
\(\tan(\pi+\alpha)=\tan\alpha\)
\(\cot(\pi+\alpha)=\cot\alpha\)

Cung phụ
\(\sin(\frac{\pi}{2}-\alpha)=\cos\alpha\)
\(\cos(\frac{\pi}{2}-\alpha)=\sin\alpha\)
\(\tan(\frac{\pi}{2}-\alpha)=\cot\alpha\)
\(\cot(\frac{\pi}{2}-\alpha)=\tan\alpha\)

Cung phụ hơn kém \(\frac{\pi}{2}\)
\(\sin(\frac{\pi}{2}+\alpha)=\cos\alpha\)
\(\cos(\frac{\pi}{2}+\alpha)=-\sin\alpha\)
\(\tan(\frac{\pi}{2}+\alpha)=-\cot\alpha\)
\(\cot(\frac{\pi}{2}+\alpha)=-\tan\alpha\)