The average of the numbers nsin⁡n∘ where $$n=2$$,$$4$$,$$6$$,…$$180$$∘ is

Question

The average of the numbers nsin⁡n∘ where $$n=2$$,$$4$$,$$6$$,…$$180$$∘ is

Infinity Learn · Accepted Answer

$$Sn=2sin$$⁡$$2$$∘$$+4sin$$⁡$$4$$∘$$+$$…$$+180sin$$⁡$$180$$∘$$Sn=2sin$$⁡$$2$$∘$$+4sin$$⁡$$4$$∘$$+$$…$$+178sin$$⁡$$178$$∘$$=2sin$$⁡$$2$$∘$$+4sin$$⁡$$4$$∘$$+$$.....$$+$$ $$178sin$$⁡$$178$$∘$$+90=2sin$$⁡$$2$$∘$$+4sin$$⁡$$4$$∘$$+$$…$$176sin4$$°$$+178sin$$⁡$$2$$∘$$+90=180sin$$⁡$$2$$∘$$+$$$$sin$$⁡$$4$$∘$$+$$…$$+$$$$sin$$⁡$$88$$∘$$+90=902sin1$$°$$sin2$$°$$+2sin1$$°$$sin4$$°$$+$$....$$+2sin1$$°$$sin88$$°$$sin1$$°$$+90$$ $$=90cos$$⁡$$1$$∘−$$cos$$⁡$$3$$∘$$+$$$$cos$$⁡$$3$$∘−$$cos$$⁡$$5$$∘$$+$$......$$+$$$$cos$$⁡$$87$$∘−$$cos$$⁡$$89$$∘$$sin$$⁡$$1$$∘$$+90=90cos$$⁡$$1$$∘−$$cos$$⁡$$89$$∘$$sin$$⁡$$1$$∘$$+90=90cot$$⁡$$1$$∘−$$1+90=90cot$$⁡$$1$$∘−$$90+90=90cot$$⁡$$1$$∘ Average $$=90cot$$⁡$$1$$∘$$90=$$$$cot$$⁡$$1$$∘

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$The average of the numbers n \sin n^{\circ} where n = 2, 4, 6, \dots 180^{\circ} is$

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Means - A.M/G.M/H.M

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The average of the numbers nsin⁡n∘ where n=2,4,6,…180∘ is

Ready to Test Your Skills?

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$The average of the numbers n \sin n^{\circ} where n = 2, 4, 6, \dots 180^{\circ} is$