SOLUTION: Find the amplitude and period of: 2 cos4t+ 5 sin4t, show steps.

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Question 351524: Find the amplitude and period of: 2 cos4t+ 5 sin4t, show steps.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Look at A%2Asin%28x%2By%29
A%2Asin%28x%2By%29=A%2Acos%28y%29sin%28x%29%2BA%2Acos%28x%29sin%28y%29%0D%0A
A%2Asin%284t%2Bb%29=A%2Acos%28b%29sin%284t%29%2BA%2Acos%284t%29sin%28b%29%0D%0A
Solve for A and b.
Comparing terms,
A%2Acos%28b%29=5
A%2Asin%28b%29=2
tan%28b%29=%282%2F5%29
b=atan%282%2F5%29
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If tan%28b%29=2%2F5, then cos%28b%29=5%2Fsqrt%282%5E2%2B5%5E2%29=5%2Fsqrt%2829%29
A%2Acos%28atan%282%2F5%29%29=5
A=5%2Fcos%28atan%282%2F5%29%29=5%2F%285%2Fsqrt%2829%29%29=sqrt%2829%29
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2+cos4t%2B+5+sin4t=sqrt%2829%29%2Asin%284t%2Batan%282%2F5%29%29
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Amplitude : A=sqrt%2829%29
Period: P=2%2Api%2F%284%29=pi%2F2