SOLUTION: If sin(A)=-5/13. Find: 1. cos(2A) 2. sin(2A) 2. Cos(4A)

Algebra ->  Trigonometry-basics -> SOLUTION: If sin(A)=-5/13. Find: 1. cos(2A) 2. sin(2A) 2. Cos(4A)      Log On


   



Question 1110589: If sin(A)=-5/13. Find:
1. cos(2A)
2. sin(2A)
2. Cos(4A)

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
If sin(A)=-5/13. Find:
1. cos(2A)
2. sin(2A)
2. Cos(4A)
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Step 1, find cos(A)
cos(A) = sqrt(1 - sin^2) = 12/13 or -12/13
The sine is negative in Q3 and Q4. The cosine is negative in Q3 and + in Q4, so the sign and quadrant cannot be determined.
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sin(2A) = 2sin(A)*cos(A)
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cos(2A) = sqrt(1 - sin^2(2A))
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cos(4A) = cos^2(2A) - sin^2(2A)