Value of sin 10°+ sin 20°+ sin 30°+ ldots ldots+ sin 360° is

Question

Value of sin 10°+ sin 20°+ sin 30°+ ldots ldots+ sin 360° is (A) 1 (B) 0 (C) 2 (D) (1/2)

Tardigrade Admin · Accepted Answer

∵ sin 190°= sin (180°+10°)=- sin 10° sin 200°=- sin 20° sin 210°=- sin 30° ........................ ..................... sin 360°= sin 180°=0 ∴ given expression =0

Q. Value of $sin 1 0^{\circ} + sin 2 0^{\circ} + sin 3 0^{\circ} + \dots\dots + sin 36 0^{\circ}$ is

1

0

2

$\frac{1}{2}$

$∵ sin 19 0^{\circ} = sin (18 0^{\circ} + 1 0^{\circ}) = - sin 1 0^{\circ}$
$sin 20 0^{\circ} = - sin 2 0^{\circ}$
$sin 21 0^{\circ} = - sin 3 0^{\circ}$
........................ .....................
$sin 36 0^{\circ} = sin 18 0^{\circ} = 0$
$∴$ given expression $= 0$

Q. Value of sin10∘+sin20∘+sin30∘+……+sin360∘ is

1

0

2

21​

∵sin190∘=sin(180∘+10∘)=−sin10∘ sin200∘=−sin20∘ sin210∘=−sin30∘ ........................ ..................... sin360∘=sin180∘=0 ∴ given expression =0

Q. Value of $sin 1 0^{\circ} + sin 2 0^{\circ} + sin 3 0^{\circ} + \dots\dots + sin 36 0^{\circ}$ is

$\frac{1}{2}$

$∵ sin 19 0^{\circ} = sin (18 0^{\circ} + 1 0^{\circ}) = - sin 1 0^{\circ}$
$sin 20 0^{\circ} = - sin 2 0^{\circ}$
$sin 21 0^{\circ} = - sin 3 0^{\circ}$
........................ .....................
$sin 36 0^{\circ} = sin 18 0^{\circ} = 0$
$∴$ given expression $= 0$