document.write( "Question 981307: Write in the form y= Asin(Bt+ ø): \r
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Algebra.Com's Answer #602325 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Instead of doing your problem I'll do one exactly in every detail\r\n" );
document.write( "like your problem.  I do this to prevent students from ignoring\r\n" );
document.write( "what we do on here and look only at the answer in attempt to fool\r\n" );
document.write( "a teacher into thinking they did the problem themselves.  So instead\r\n" );
document.write( "of f(t) = 8sint+6cost, I will do the problem for f(t) = 15sint+8cost.  \r\n" );
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document.write( "y= Asin(Bt+ø) \r\n" );
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document.write( "let y = f(t) and use the double angle sine formula:\r\n" );
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document.write( "f(t) = Asin(Bt+ø)\r\n" );
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document.write( "f(t) = Asin(Bt)cos(ø)+ Acos(Bt)sin(ø)\r\n" );
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document.write( "We compare that to\r\n" );
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document.write( "f(t) = 15sin(t) + 8cos(t)\r\n" );
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document.write( "Its obvious that we can let B=1. So we have:\r\n" );
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document.write( "f(t) = Asin(t+ø)\r\n" );
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document.write( "f(t) = Asin(t)cos(ø) + Acos(t)sin(ø)\r\n" );
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document.write( "f(t) = 15sin(t) + 8cos(t)\r\n" );
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document.write( "Equating corresponding terms:\r\n" );
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document.write( " 15sin(t) = Asin(t)cos(ø)         8cos(t) = Acos(t)sin(ø)\r\n" );
document.write( "       15 = Acos(ø)                     8 = Asin(ø)\r\n" );
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document.write( "Divide equals by equals and get equals:\r\n" );
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document.write( "     \"8%2F15\"\"%22%22=%22%22\"\"%28A%2Asin%28phi%29%29%2F%28A%2Acos%28phi%29%29\"\r\n" );
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document.write( "     \"8%2F15\"\"%22%22=%22%22\"\"sin%28phi%29%2Fcos%28phi%29\"\r\n" );
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document.write( "     \"8%2F15\"\"%22%22=%22%22\"\"tan%28phi%29\"\r\n" );
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document.write( "     \"%2228.07248694%B0%22\"\"%22%22=%22%22\"\"phi\"\r\n" );
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document.write( "Now we draw a right triangle that has an angle with tangent of 8/15.\r\n" );
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document.write( "We do that by putting 8 on the opposite side and 15 on the adjacent\r\n" );
document.write( "side, so that \"tan%28phi%29=%28opposite%29%2F%28adjacent%29=8%2F15\", and we use the \r\n" );
document.write( "Pythagorean theorem to find the hypotenuse\r\n" );
document.write( "\"c%5E2=a%5E2%2Bb%5E2\"\r\n" );
document.write( "\"c%5E2=8%5E2%2B15%5E2\"\r\n" );
document.write( "\"c%5E2=64%2B225\"\r\n" );
document.write( "\"c%5E2=289\"\r\n" );
document.write( "\"c=17\"\r\n" );
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document.write( "From that triangle, cos(ø) = 15/17 \r\n" );
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document.write( "15 = Acos(ø)\r\n" );
document.write( "\"15+=+A%2815%2F17%29\"\r\n" );
document.write( "\"15%2A17+=+15A\"\r\n" );
document.write( "\"17=A\" \r\n" );
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document.write( "\"%2228.07248694%B0%22\"\"%22%22=%22%22\"\"phi\"\r\n" );
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document.write( "So the answer is found by substituting in:\r\n" );
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document.write( "f(t) = Asin(t+ø)\r\n" );
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document.write( "f(t) = 17sin(t+28.07248694°)\r\n" );
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document.write( "Now do yours EXACTLY like this one.\r\n" );
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document.write( "Edwin
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