document.write( "Question 73908This question is from textbook
\n" ); document.write( ": Find all solutions to the equation sin x = 0.
\n" ); document.write( "a. x = \"PI\"n
\n" ); document.write( "b. x = 2\"PI\"n
\n" ); document.write( "c. x = \"PI%2F2+%2B+PI\"n
\n" ); document.write( "d. x = \"PI\" + 2 \"PI\"n \n" ); document.write( "
Algebra.Com's Answer #52954 by bucky(2189)\"\" \"About 
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Find all solutions to sin x = 0
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\n" ); document.write( "Answer \"a\" is the correct selection for this problem.
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\n" ); document.write( "Probably the best way to work this problem is to look at the answers and evaluate them one at
\n" ); document.write( "a time to see if the sine they produce actually does equal zero.
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\n" ); document.write( "Another thing that might help you is to recognize that \"pi\" is equivalent to 180 degrees.
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\n" ); document.write( "It always helped me to use the definitions of trig functions to evaluate the values of
\n" ); document.write( "those functions. For example, in this problem you are interested in the sine function
\n" ); document.write( "and it is defined as the ratio of the side opposite divided by the hypotenuse. So when will
\n" ); document.write( "the sine be equal to zero? That will occur when the side opposite disappears and thinking
\n" ); document.write( "of the angle being in standard position in the first quadrant, the side opposite gets smaller
\n" ); document.write( "and smaller as the angle goes towards 0 degrees (or 0 radians). The sine finally reaches
\n" ); document.write( "0 at 0 degrees or zero radians. The same thing happens as the angle approaches pi radians
\n" ); document.write( "or 180 degrees. The side opposite approaches 0 until at pi radians or 180 degrees it
\n" ); document.write( "actually is 0 and therefore the \"sin%28pi%29+=+0\".
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\n" ); document.write( "Another way you can view this is to think of the sine wave plot. It starts at 0, rises to
\n" ); document.write( "a peak at \"pi%2F2\" or 90 degrees, then falls back to zero at \"pi\" or 180 degrees,
\n" ); document.write( "then falls further to a minimum at \"3pi%2F2\" or 270 degrees and then rises to again be zero
\n" ); document.write( "at \"2pi\" or 360 degrees.
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\n" ); document.write( "So we have sin(x) equal to zero at 0 and \"pi\" or 180 degrees and \"2pi\" or 360 degrees
\n" ); document.write( "and every additional \"pi\" or 180 degrees thereafter.
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\n" ); document.write( "Note that answer \"a\" meets that requirement as long as n = 0,1,2,3,4,5,...
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\n" ); document.write( "Answer b will not work because it is multiples of \"2pi\". When n = 0 it works, but
\n" ); document.write( "when n = 1 it is at \"2pi\" or 360 degrees. It completely skipped over the fact that
\n" ); document.write( "\"sin%28pi%29=+0\".
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\n" ); document.write( "Answer c will not work. When n = 0 the angle is \"pi%2F2\" or 90 degrees. The value of
\n" ); document.write( "\"sin%28pi%2F2%29\" or its equivalent \"sin%2890%29\" is 1, not zero.
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\n" ); document.write( "Answer d will not work. When n = 0 the angle becomes \"pi\" (or 180 degrees) and for each
\n" ); document.write( "increase in n you add \"2pi\" or 360 degrees. So the angles it generates are \"pi\" (180 degrees),
\n" ); document.write( "\"3pi\" (540), \"5pi\" (900) ... It completely misses the angles 0, \"2pi\" (360 degrees),
\n" ); document.write( "\"4pi\" (720), \"6pi\" (1080) ...
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\n" ); document.write( "Hope this discussion helps you to become more familiar with trig functions and angles.
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