document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156473>Question 1156473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Pythagorean identities to write the expression as an integer.<BR>\n" );
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document.write( "7 sin^2 θ + 7 cos^2 θ\r<BR>\n" );
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document.write( "(b)    <BR>\n" );
document.write( "7 sin2(θ/4) + 7 cos2(θ/4)\r<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 #779173 by </B><A HREF=/tutors/aboutme.mpl?userid=Shin123><B>Shin123(626)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Shin123><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=Shin123><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Suppose a right triangle has hypotenuse 1 and one angle that is not the right angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" >. By the definition of sine and cosine, the legs have lengths <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28theta%29 ALIGN=MIDDLE  ALT=\"sin%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28theta%29 ALIGN=MIDDLE  ALT=\"cos%28theta%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. By the Pythagorean Theorem, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiplying both sides by 7 gets <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Asin%5E2%28theta%29%2B7%2Acos%5E2%28theta%29=7 ALIGN=MIDDLE  ALT=\"7%2Asin%5E2%28theta%29%2B7%2Acos%5E2%28theta%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "b) Dividing <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > by 4 in part a) gets <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Asin%5E2%28theta%2F4%29%2B7%2Asin%5E2%28theta%2F4%29=7 ALIGN=MIDDLE  ALT=\"7%2Asin%5E2%28theta%2F4%29%2B7%2Asin%5E2%28theta%2F4%29=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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