document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203872>Question 1203872</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the given function value and the trigonometric identities to find the exact value of each indicated trigonometric function \r<BR>\n" );
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document.write( "0° ≤ 𝛼 ≤ 90°, 0 ≤ 𝛼 ≤ <BR>\n" );
document.write( "𝜋<BR>\n" );
document.write( "2\r<BR>\n" );
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document.write( "cot(𝛼) = 3<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "tan(𝛼)<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "csc(𝛼)<BR>\n" );
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document.write( "(c)<BR>\n" );
document.write( "sec(𝛼)<BR>\n" );
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document.write( "(d)<BR>\n" );
document.write( "sin(𝛼)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839747 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given that cot(theta) = 3<BR>\n" );
document.write( "cot(theta) = adjacent side divided by opposite side.\r<BR>\n" );
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document.write( "if adjacent side is 3, then opposite side is 1.<BR>\n" );
document.write( "use pythagorus to solve for hypotenuse.<BR>\n" );
document.write( "pythagorus says that hypotenuse squared = adjacent side squared plus opposite side square.<BR>\n" );
document.write( "you get hypotenuse squared = 3^2 + 1^2 = 9 + 1 = 10<BR>\n" );
document.write( "this makes hypotenuse = sqrt(10)<BR>\n" );
document.write( "you have:<BR>\n" );
document.write( "adjacent side = 3<BR>\n" );
document.write( "opposite side = 1<BR>\n" );
document.write( "hypotenuse = 10\r<BR>\n" );
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document.write( "(a)<BR>\n" );
document.write( "tan(𝛼) = opposite side / adjacent side = 1/3\r<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "csc(𝛼) = hypotenuse / opposite side = sqrt(10)/1 = sqrt(10)\r<BR>\n" );
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document.write( "(c)<BR>\n" );
document.write( "sec(𝛼) = hypotenuse / adjacent side = sqrt(10)/3\r<BR>\n" );
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document.write( "(d)<BR>\n" );
document.write( "sin(𝛼) = opposite side / hypotenuse = 1/sqrt(10)\r<BR>\n" );
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document.write( "here's a diagram with all the basic trig functions identified.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/092406.jpg\">\r<BR>\n" );
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document.write( " </SPAN>\n" );
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