Evaluating $sin 10^circ + sin 20^circ + sin 30^circ + cdots +sin 90^circ$

The question is finding
$$S = sin 10^circ + sin 20^circ + sin 30^circ + cdots +sin 90^circ$$

I tried to do it, but I can’t eliminate the $cos 5^circ$.

Can anyone help me with the answer?

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Mathematics Asked by Crevious on December 31, 2020

1 Answers

One Answer

Best it is to follow symbolic derivation of sums of sine of $n$ angles in A.P, of common difference $beta= 10^{circ}.$ And then apply it.

$$ S = sin ( average; angle)cdot dfrac{sin n beta/2}{sin beta/2}$$

$$={ sin 50^{circ}}dfrac{ sin 9times 5^{circ}}{sin 5^{circ}}.$$

Correct answer by Narasimham on December 31, 2020

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