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Question

If $sin space pi over 18 sin space fraction numerator 5 pi over denominator 18 end fraction sin space fraction numerator 7 pi over denominator 18 end fraction$ =

8
$- \frac{7}{8}$
$- \frac{9}{8}$
$\frac{1}{8}$

hint Hint:

Convert $straight pi over 180$ into normal form.

The correct answer is: $negative 9 over 8$

$sin space pi over 18 sin space fraction numerator 5 pi over denominator 18 end fraction sin space fraction numerator 7 pi over denominator 18 end fraction open parentheses pi over 18 equals 10 degree close parentheses equals sin space 10 degree sin space 50 degree sin space 70 degree equals 1 half open parentheses sin space 10 degree 2 sin space 50 degree sin space 70 degree close parentheses equals fraction numerator sin 10 degree over denominator 2 end fraction open parentheses cos open parentheses 70 degree minus 50 degree close parentheses plus cos open parentheses 70 degree plus 50 degree close parentheses close parentheses equals fraction numerator sin 10 degree over denominator 2 end fraction open parentheses cos open parentheses 20 degree close parentheses plus cos open parentheses 120 degree close parentheses close parentheses equals fraction numerator sin 10 degree over denominator 2 end fraction open parentheses 1 minus 2 sin squared open parentheses 10 degree close parentheses plus 1 half close parentheses open parentheses because cos 2 x equals 1 minus 2 sin squared x close parentheses equals fraction numerator sin 10 degree over denominator 2 end fraction open parentheses fraction numerator 3 minus 4 sin squared open parentheses 10 degree close parentheses over denominator 2 end fraction close parentheses equals 1 fourth open parentheses 3 sin 10 degree minus 4 sin cubed 10 degree close parentheses equals 1 fourth open parentheses sin 30 degree close parentheses equals 1 fourth cross times 1 half equals 1 over 8$

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