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Find the exact value of sin(-15)

User Uupascal
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2 Answers

3 votes

Answer:


(√(6) - √(2) )/(4) is the answer

Explanation:

I just took the test, and did the calculations.

User Zev Isert
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6 votes

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- ( √(3) )/(2) }}{\big{2}}} =-\sqrt{\frac{\big{2- √(3)}}{\big{4}}} =\\\\ =- (1)/(2) \sqrt{2- √(3)}
User Emil Ivanov
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