1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of the sin 1° + sin 2° +......+ sin 359° is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The value of the $\sin \; 1^{\circ} + \sin \; 2^{\circ} +......+ \sin 359^{\circ}$ is equal to

KCETKCET 2016Trigonometric Functions

Solution:

$ \sin 1^{\circ}+\sin 2^{\circ}+\sin 3^{\circ}+\ldots+\sin 359^{\circ} $
$=\left(\sin 1^{\circ}+\sin 359^{\circ}\right)+\left(\sin 2^{\circ}+\sin 358^{\circ}\right)+\ldots +\sin 180^{\circ} $
$=0+0+0+\ldots+0=0$
$ \left[\because \sin \theta+\sin \left(360^{\circ}-\theta\right)=0\right] $