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ddd [48]
3 years ago
11

What is the exact value of sin(5π/12)? (please give steps)​

Mathematics
1 answer:
snow_tiger [21]3 years ago
7 0

Answer:

0.966053748

Step-by-step explanation:

\sin \bigg( \frac{5\pi}{12} \bigg) \\  =  \sin \bigg( \frac{5 \times 180 \degree}{12} \bigg) \\  =   \sin ( 5 \times 15 \degree) \\  =  \sin ( 75 \degree) \\  = \sin ( 45 \degree + 30 \degree) \\  = \sin  45 \degree  \times  \cos 30 \degree + \cos  45 \degree  \times  \sin 30 \degree \\  \\  =  \frac{1}{ \sqrt{2} }  \times   \frac{ \sqrt{3} }{2}  +  \frac{1}{ \sqrt{2} }  \times  \frac{1}{2}  \\  \\  =  \frac{ \sqrt{3} }{2 \sqrt{2} }  +  \frac{1}{2 \sqrt{2} }  \\  \\  =  \frac{ \sqrt{3}  + 1}{2 \sqrt{2} }  \\  \\  =  \frac{1.732 + 1}{2 \times 1.414}  \\  \\  =  \frac{2.732}{2.828}  \\  \\  = 0.966053748

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