a) Hai góc đối nhau $\alpha$ và $-\alpha$

$\sin (-\alpha )=-\sin \alpha$;

$\cos (-\alpha )=\cos \alpha$;

$\tan (-\alpha )=-\tan \alpha$;

$\cot (-\alpha )=-\cot \alpha$.

b) Hai góc phụ nhau $\alpha$ và ${90}^o-\alpha$

$\sin \left({90}^o-\alpha \right)=\cos \alpha$;

$\cos \left({90}^o-\alpha \right)=\sin \alpha$;

$\tan \left({90}^o-\alpha \right)=\cot \alpha$;

$\cot \left({90}^o-\alpha \right)=\tan \alpha$.

c) Hai góc bù nhau $\alpha$ và ${180}^o-\alpha$

$\sin \left({180}^o-\alpha \right)=\sin \alpha$;

$\cos \left({180}^o-\alpha \right)=-\cos \alpha$;

$\tan \left({180}^o-\alpha \right)=-\tan \alpha$;

$\cot \left({180}^o-\alpha \right)=-\cot \alpha$.

d) Hai góc $\alpha$ và ${90}^o+\alpha$

$\sin \left({90}^o+\alpha \right)=\cos \alpha$;

$\cos \left({90}^o+\alpha \right)=-\sin \alpha$;

$\tan \left({90}^o+\alpha \right)=-\cot \alpha$;

$\cot \left({90}^o+\alpha \right)=-\tan \alpha$.

e) Hai góc $\alpha$ và ${180}^o+\alpha$

$\sin \left({180}^o+\alpha \right)=-\sin \alpha$;

$\cos \left({180}^o+\alpha \right)=-\cos \alpha$;

$\tan \left({180}^o+\alpha \right)=\tan \alpha$;

$\cot \left({180}^o+\alpha \right)=\cot \alpha$.

1) Cho tam giác ABC, khi đó ta có:

$\sin A=\sin ({180}^o-A)=\sin (B+C)$;

$\sin \frac{A}{2}=\cos \left({90}^o-\frac{A}{2}\right)=\cos \left(\frac{B+C}{2}\right)$.

2) Tính các giá trị lượng giác $\sin {570}^o$, $\cos (-{1035}^o)$, $\tan {1500}^o$.

Giải:

$\sin {570}^o=\sin ({360}^o+{180}^o+{30}^o)=\sin ({180}^o+{30}^o)=-\sin {30}^o=-\frac{1}{2}$.

$\cos (-{1035}^o)=\cos (-{\mathrm{3.2.180}}^o+{45}^o)=\cos \left({45}^o\right)=\frac{\sqrt{2}}{2}$.

$\tan \left({1500}^o\right)=\tan ({8.180}^o+{60}^o)=\tan \left({60}^o\right)=\sqrt{3}$.