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inessss [21]
3 years ago
12

Find the exact value of sin(-15)

Mathematics
1 answer:
koban [17]3 years ago
7 0
1)\ \ \ sin(- \alpha )=-sin \alpha \\2)\ \ \ cos2 \alpha =1-2sin^2 \alpha \ \ \ \Rightarrow\ \ \ 2sin^2 \alpha =1-cos2 \alpha \\\\ \Rightarrow\ \ \ sin \alpha = \sqrt{\frac{\big{1-cos2 \alpha}}{\big{2}}}  \\\\\\sin(-15^0)=-sin15^0=-\sqrt{\frac{\big{1-cos30^0}}{\big{2}}}  =-\sqrt{\frac{\big{1- \frac{ \sqrt{3} }{2} }}{\big{2}}} =-\sqrt{\frac{\big{2- \sqrt{3}}}{\big{4}}} =\\\\ =- \frac{1}{2}  \sqrt{2- \sqrt{3}}
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