document.write( "Question 1205013: The graph shows part of a sine function of the form y = A sin B(x + C) + D. Determine the values of A, B, C, and D.
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\n" ); document.write( "\n" ); document.write( "The answer key is A = 2, B = 3, C = -π/3, D = -1\r
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\n" ); document.write( "\n" ); document.write( "Is y = A sin B(x + C) + D the same as y = asin(bx - c) + d? I'm confused. I don't understand why the first formula has \"+ C\" instead of \"- c\". I thought the formula of the parent graph is always written \"- c\" regardless if the value of c is negative or positive. I understood that only after replacing the variables with values and if \"c\" has a negative value and you are subtracting a negative (double negatives) that it becomes addition, but why is the first formula with variables \"+ C\" instead of \"- c\"? And why is \"B\" outside the parenthesis instead of inside? I thought \"b\" was supposed to be a quotient of \"x\". \n" ); document.write( "

Algebra.Com's Answer #841612 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Hello, other tutors wrote many words, but they did not answer your question.\r
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document.write( "Look at the plot.\r\n" );
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document.write( "You see sinusoidal periodical curve.\r\n" );
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document.write( "You may move/shift it one period to the right (by subtracting the period from the argument) - \r\n" );
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document.write( "          - you will get the same curve, since the function is periodical.\r\n" );
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document.write( "You may move/shift it one period to the left (by adding the period to the argument) - \r\n" );
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document.write( "          - you will get the same curve, since the function is periodical.\r\n" );
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document.write( "It explains WHY you may have THE SAME CURVE, even although you have positive argument in one form, but negative argument in other form.\r\n" );
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document.write( "Different formulas for sine function describe THE SAME CURVE, if the arguments differ by integer number of periods.\r\n" );
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document.write( "So, different values of the sine argument may describe (and do describe) the same curve, \r\n" );
document.write( "if the arguments differ by integer values of periods.\r\n" );
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document.write( "It is common property of all periodic functions : sin(x), cos(x), tan(x), sec(x), csc(x), \r\n" );
document.write( ", , , sin(x)*cos(x),   etc.\r\n" );
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