SOLUTION: If and sin∝=4/5, and ∝ is an acute angle, find the exact value of sin 2∝

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Question 1171118: If and sin∝=4/5, and ∝ is an acute angle, find the exact value of sin 2∝
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
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If and sin(a)=4/5, and "a" is an acute angle, find the exact value of sin 2a.
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If sin(a) = 4%2F5,  then cos(a) = sqrt%281-sin%5E2%28a%29%29 = sqrt%281-%284%2F5%29%5E2%29 = sqrt%28%2825-16%29%2F25%29 = sqrt%289%2F25%29 = 3%2F5.


and we use the positive value of the square root, since the angle "a" is acute.


Next,  sin(2a) = one of the basic formula of Trigonometry = 2*sin(a)*cos(a) = 2%2A%284%2F5%29%2A%283%2F5%29 = 24%2F25.    ANSWER

Solved.