document.write( "Question 351524: Find the amplitude and period of: 2 cos4t+ 5 sin4t, show steps. \n" ); document.write( "

Algebra.Com's Answer #251291 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Look at $\"A%2Asin%28x%2By%29\"$
\n" ); document.write( " $\"A%2Asin%28x%2By%29=A%2Acos%28y%29sin%28x%29%2BA%2Acos%28x%29sin%28y%29%0D%0A\"$
\n" ); document.write( " $\"A%2Asin%284t%2Bb%29=A%2Acos%28b%29sin%284t%29%2BA%2Acos%284t%29sin%28b%29%0D%0A\"$
\n" ); document.write( "Solve for $\"A\"$ and $\"b\"$ .
\n" ); document.write( "Comparing terms,
\n" ); document.write( " $\"A%2Acos%28b%29=5\"$
\n" ); document.write( " $\"A%2Asin%28b%29=2\"$
\n" ); document.write( " $\"tan%28b%29=%282%2F5%29\"$
\n" ); document.write( " $\"b=atan%282%2F5%29\"$
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\n" ); document.write( "If $\"tan%28b%29=2%2F5\"$ , then $\"cos%28b%29=5%2Fsqrt%282%5E2%2B5%5E2%29=5%2Fsqrt%2829%29\"$
\n" ); document.write( " $\"A%2Acos%28atan%282%2F5%29%29=5\"$
\n" ); document.write( " $\"A=5%2Fcos%28atan%282%2F5%29%29=5%2F%285%2Fsqrt%2829%29%29=sqrt%2829%29\"$
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\n" ); document.write( " $\"2+cos4t%2B+5+sin4t=sqrt%2829%29%2Asin%284t%2Batan%282%2F5%29%29\"$
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\n" ); document.write( "Amplitude : $\"A=sqrt%2829%29\"$
\n" ); document.write( "Period: $\"P=2%2Api%2F%284%29=pi%2F2\"$ \r
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