Find-the-value-of-S-where-S-r-1-89-sin-6-r-

Question Number 4600 by Yozzii last updated on 11/Feb/16

Find the value of S where S=Σ_(r=1) ^(89) sin^6 r°.

$${Find}\:{the}\:{value}\:{of}\:{S}\:{where}\:{S}=\underset{{r}=\mathrm{1}} {\overset{\mathrm{89}} {\sum}}{sin}^{\mathrm{6}} {r}°. \\ $$

Commented by FilupSmith last updated on 11/Feb/16

Don′t you use the series representation for sine?

$$\mathrm{Don}'\mathrm{t}\:\mathrm{you}\:\mathrm{use}\:\mathrm{the}\:\mathrm{series}\:\mathrm{representation} \\ $$$$\mathrm{for}\:\mathrm{sine}? \\ $$

Commented by Yozzii last updated on 11/Feb/16

$${That}'{s}\:{not}\:{necessary}\:{here}.\: \\ $$

Commented by Yozzii last updated on 12/Feb/16

Try using the fact that sin(90−α°)=cosα , α∈R.

$${Try}\:{using}\:{the}\:{fact}\:{that} \\ $$$${sin}\left(\mathrm{90}−\alpha°\right)={cos}\alpha\:,\:\alpha\in\mathbb{R}. \\ $$

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