document.write( "Question 887545: given that cos2a =2/5 and 0<2a<90, determine the exact values of sin a, cos a, tan a, csc a, sec a, and cot a. \n" ); document.write( "
Algebra.Com's Answer #536718 by Edwin McCravy(20059)\"\" \"About 
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document.write( "Since a is in the first quadrant, everything will be positive, so\r\n" );
document.write( "when we take square roots we only need to take positive square\r\n" );
document.write( "roots.\r\n" );
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document.write( "\"cos%282a%29+=+2%2F5\"\r\n" );
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document.write( "Use the identity \"cos%282a%29=2cos%5E2%28a%29-1\"\r\n" );
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document.write( "\"2%2F5=2cos%5E2%28a%29-1\"\r\n" );
document.write( "\"2=10cos%5E2%28a%29-5\"\r\n" );
document.write( "\"7=10cos%5E2%28a%29\"\r\n" );
document.write( "\"7%2F10=cos%5E2%28a%29\"\r\n" );
document.write( "\"sqrt%287%2F10%29=cos%28a%29\", that's the cosine.\r\n" );
document.write( "You can rationalize the denominator if you like.\r\n" );
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document.write( "Then use the identity \"sec%28a%29=1%2Fcos%28a%29\"\r\n" );
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document.write( "\"sec%28a%29=sqrt%2810%2F7%29\"\r\n" );
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document.write( "Use the identity: \"sin%5E2%28a%29%2Bcos%5E2%28a%29=1\"\r\n" );
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document.write( "\"sin%5E2%28a%29%2B7%2F10=1\"\r\n" );
document.write( "\"sin%5E2%28a%29=3%2F10\"\r\n" );
document.write( "\"sin%28a%29=sqrt%283%2F10%29\", that's the sine.\r\n" );
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document.write( "Then use the identity \"csc%28a%29=1%2Fsin%28a%29\"\r\n" );
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document.write( "\"csc%28a%29=sqrt%2810%2F3%29\", that's the cosecant.\r\n" );
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document.write( "Use the identity \"tan%28a%29=sin%28a%29%2Fcos%28a%29\" \r\n" );
document.write( "  \r\n" );
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document.write( "\"tan%28a%29=sqrt%283%2F7%29\", that's the tangent\r\n" );
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document.write( "Use the identity \"cot%28a%29=1%2Ftan%28a%29\" \r\n" );
document.write( "  \r\n" );
document.write( "\"cot%28a%29=sqrt%287%2F3%29\", that's the cotangent.\r\n" );
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document.write( "So that's all six.\r\n" );
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document.write( "Edwin

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