sin 10°+sin 20°+ sin 30°+.......+ sin 360° is equal to
a. 0
b. 1
c. -1
d. 1/2
Explain.
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Answer: Zero
Solution:
i) There are 36 terms;
ii) Group them as: (sin10° + sin350°) + (sin20° + sin340°) + (sin30° + sin330°) + ....
+ .. + (sin170° + sin190°) + (sin180° + sin360°)
This forms to 18 pairs.
Each pair is zero.
sin10° + sin350° = sin10° + sin(360 - 10) = sin10° - sin10° = 0
Like this every pair becomes zero.
Thus total sum is zero.
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