document.write( "Question 189534: sin theta= 12/13, 3pi/2\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( "cos-1/4,csc theta>0, find sin 2theta,cos 2theta, tan 2theta \n" ); document.write( "
Algebra.Com's Answer #142212 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I can do your 2nd problem but not the 1st, for you've \r\n" );
document.write( "made a mistake in copying the first problem. Here's why:\r\n" );
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document.write( "sinq = 12/13, 3p/2 < q < 2p. Find sin2q, cos2q, tan2q?\r\n" );
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document.write( "3p/2 < q < 2p\r\n" );
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document.write( "tells us that q is in quadrant IV.\r\n" );
document.write( "But the sine is negative in quadrant IV, yet you have \r\n" );
document.write( "sinq = 12/13, which is a positive number.\r\n" );
document.write( "That cannot be.\r\n" );
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document.write( "Here's your 2nd problem:\r\n" );
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document.write( "cosq = -1/4,cscq > 0, find sin2q,cos2q, tan2q\r\n" );
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document.write( "This tells us that q is in quadrant II,\r\n" );
document.write( "because that is the only quadrant in which the cosine is negative and\r\n" );
document.write( "the cosecant is positive.\r\n" );
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document.write( "So we draw an angle in Quadrant II to represent angle q \r\n" );
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document.write( "Next we draw a perpendicular to the x axis.  Since the cosine\r\n" );
document.write( "is \"x%2Fr\", we make the x value -1, which is the numerator of \r\n" );
document.write( "\"%28-1%29%2F4\" and make the hypotenuse or the r equal to the the \r\n" );
document.write( "denominator of \"%28-1%29%2F4\" which is 4: \r\n" );
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document.write( "Next we calculate the value of y by the Pythagorean\r\n" );
document.write( "theorem equation\r\n" );
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document.write( "\"x%5E2%2By%5E2=r%5E2\"\r\n" );
document.write( "\"%28-1%29%5E2%2By%5E2=%284%29%5E2\"\r\n" );
document.write( "\"1%2By%5E2=16\"\r\n" );
document.write( "\"y%5E2=15\"\r\n" );
document.write( "\"y=sqrt%2815%29\"\r\n" );
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document.write( "So we label the y-value with that\r\n" );
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document.write( "Now we can find sin2q using the\r\n" );
document.write( "identity:\r\n" );
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document.write( "sin2q = 2sinqcosq\r\n" );
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document.write( "because we now know that sinq = \"y%2Fr\" = \"sqrt%2815%29%2F4\", and cosq = \"x%2Fr\" = \"-1%2F4\".\r\n" );
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document.write( "sin2q = 2sinqcosq = \"2%28sqrt%2815%29%2F4%29%28-1%2F4%29=-2sqrt%2815%29%2F16=-sqrt%2815%29%2F8\"\r\n" );
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document.write( "Next we find cos2q using any one of\r\n" );
document.write( "these three identities:\r\n" );
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document.write( "cos2q = cos2q - sin2q\r\n" );
document.write( "cos2q = 2cos2q - 1\r\n" );
document.write( "cos2q = 1 - 2sin2q.\r\n" );
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document.write( "I'll choose the second one, although any one will give you the\r\n" );
document.write( "same answer:\r\n" );
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document.write( "cos2q = 2cos2q - 1\r\n" );
document.write( "cos2q = 2\"%28-1%2F4%29%5E2\" - 1\r\n" );
document.write( "cos2q = 2\"1%2F16\" - 1\r\n" );
document.write( "cos2q = \"2%2F16\" - 1\r\n" );
document.write( "cos2q = \"1%2F8\" - 1\r\n" );
document.write( "cos2q = \"-7%2F8\"\r\n" );
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document.write( "Finally we can find tan2q from\r\n" );
document.write( "the identity\r\n" );
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document.write( "tan2q = sin2q/cos2q\r\n" );
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document.write( "tan2q = \r\n" );
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document.write( "Edwin
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