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Maths-

General

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Question

$s i n invisible function application fraction numerator pi over denominator 9 end fraction s i n invisible function application fraction numerator 2 pi over denominator 9 end fraction s i n invisible function application fraction numerator 4 pi over denominator 9 end fraction s i n invisible function application fraction numerator pi over denominator 3 end fraction text is equal to end text$

$\frac{3}{4}$
$\frac{3}{8}$
$\frac{3}{16}$
None of these

The correct answer is: $fraction numerator 3 over denominator 16 end fraction$

We have
$s i n invisible function application 20 to the power of ring operator end exponent s i n invisible function application 40 to the power of ring operator end exponent s i n invisible function application 80 to the power of ring operator end exponent s i n invisible function application 60 to the power of ring operator end exponent$
$equals fraction numerator square root of 3 over denominator 2 end fraction open square brackets s i n invisible function application 20 to the power of ring operator end exponent times s i n invisible function application open parentheses 60 to the power of ring operator end exponent minus 20 to the power of ring operator end exponent close parentheses times s i n invisible function application open parentheses 60 to the power of ring operator end exponent plus 20 to the power of ring operator end exponent close parentheses close square brackets$
$equals fraction numerator square root of 3 over denominator 2 end fraction open square brackets s i n invisible function application 20 to the power of ring operator end exponent times open parentheses s i n to the power of 2 end exponent invisible function application 60 to the power of ring operator end exponent minus s i n to the power of 2 end exponent invisible function application 20 to the power of ring operator end exponent close parentheses close square brackets$
$equals fraction numerator square root of 3 over denominator 2 end fraction open square brackets fraction numerator 3 s i n invisible function application 20 to the power of ring operator end exponent minus 4 s i n to the power of 3 end exponent invisible function application 20 to the power of ring operator end exponent over denominator 4 end fraction close square brackets$
$equals fraction numerator square root of 3 over denominator 8 end fraction times s i n invisible function application 60 to the power of ring operator end exponent equals fraction numerator 3 over denominator 16 end fraction$

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