Question

Solve $\sin {10}^o+\sin {20}^o+\sin {30}^o+...+\sin {360}^o$

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

Answer: (A)

$0$

Given

$\sin 10+\sin 20+\sin 30+..........+\sin 360$

$=\{\sin 10+\sin 20+\sin 30+...+\sin 180\}+\{\sin 190+\sin 200+\sin (180+30)...+\sin 360\}$

$=\{\sin 10+\sin 20+\sin 30+...+\sin 180\}+\left\{\sin \right(180+10)+\sin (180+20)+\sin (180+30)...+\sin (180+180\left)\right\}$

We know

$\sin (180+\theta )=-\sin \theta$

Now,

$=\{\sin 10+\sin 20+\sin 30+...+\sin 180\}+\{-\sin 10-\sin 20-\sin \mathrm{30...}-\sin 180\}$

$=\sin 10+\sin 20+\sin 30+...+\sin 180-\sin 10-\sin 20-\sin \mathrm{30...}-\sin 180$

$=0$