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kolezko [41]
4 years ago
6

What is the exact value of sin(157.5°)?

Mathematics
1 answer:
goldfiish [28.3K]4 years ago
3 0

Answer:

\frac{\sqrt{2 - \sqrt{2} } }{2}

Step-by-step explanation:

sin ^{2}  (157.5°)  =  1/2(1 - cos(2*157.5))

==>  1/2(1 - cos(315))

==>  1/2(\sqrt{2}   /2)

==>  (2 - \sqrt{2} ) / 4

sin(157.5°)  is in quadrant ll , meaning sin(157.5°) is greater than 0 , so we take positive square root of sin(157.5°)

sin(157.5) = \frac{\sqrt{2 - \sqrt{2} } }{2}

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