document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122860>Question 1122860</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Label each of the following statements as true or false.\r<BR>\n" );
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document.write( "The graph of y=cos (&#952;+ pi/2) is a reflection of the graph of y= -sin &#952; in the x-axis.\r<BR>\n" );
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document.write( "On the interval -pi < &#952; < pi, the only intersection point of the graphs of y= &#952; amd y= sin &#952; is at 0=0.\r<BR>\n" );
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document.write( "2.  Given the right triangle ABC, fill the values of sin &#952; and cos &#952;, and prove that sin^2 &#952; + cos^2 &#952;= 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739274 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=739274\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The graph of y=cos (&#952; + pi/2) is a reflection of the graph of y= -sin &#952; in the x-axis. \r<BR>\n" );
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document.write( "i would say false.\r<BR>\n" );
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document.write( "these equations are identical.\r<BR>\n" );
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document.write( "if theta = pi/4 (45 degrees), then:\r<BR>\n" );
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document.write( "cos(pi/4 + pi/2) = -.7071067812\r<BR>\n" );
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document.write( "= sin(pi/4) = -.7071067812\r<BR>\n" );
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document.write( "this occurs at all values of theta.\r<BR>\n" );
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document.write( "the equations of y = cos(theta + pi/2) and y = sin(theta) would be reflections about the line = x.\r<BR>\n" );
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document.write( "the following graphs show the relationships.\r<BR>\n" );
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document.write( "in both graphs, i used x instead of theta, since x can be graphed easier than theta.\r<BR>\n" );
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document.write( "theta and x mean the same thing.<BR>\n" );
document.write( "they are the angle being measured.\r<BR>\n" );
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document.write( "first graph is y = cos(x + pi/2) and y = -sin(x)\r<BR>\n" );
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document.write( "both equations give you the same graph which means the equations are equivalent.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/091201.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "second graph is y = cos(x + pi/2) and y = sin(x).\r<BR>\n" );
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document.write( "in this graph it is clear to see that the graph of y = sin(x) is a reflection of the graph y = cos(theta + pi/2) about the x-axis.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/091202.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "On the interval -pi < &#952; < pi, the only intersection point of the graphs of y= &#952; amd y= sin &#952; is at 0=0.\r<BR>\n" );
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document.write( "this statement is true as can be seen in the following graph.\r<BR>\n" );
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document.write( "in the graph, x represents theta.<BR>\n" );
document.write( "they mean the same thing.\r<BR>\n" );
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document.write( "you can see that when x is 0, y = sin(x) is equal to 0 and y = x is also equal to 0.\r<BR>\n" );
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document.write( "at any other point on the graph, y = x is not equal to y = sin(x).\r<BR>\n" );
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document.write( "the graph would ahow all the intersection points between the two equations and only one is shown at x = 0.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/091203.jpg\" alt=\"$$$\" >L\r<BR>\n" );
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document.write( "Given the right triangle ABC, fill the values of sin &#952; and cos &#952;, and prove that sin^2 &#952; + cos^2 &#952;= 1\r<BR>\n" );
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document.write( "in triangle ABC, side a is opposite angle A, side b is opposite angle B and side c is opposite angle C.\r<BR>\n" );
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document.write( "the hypotenuse of the triangle is the side opposite angle C which is the right angle in the triangle.\r<BR>\n" );
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document.write( "by pythagorus, c^2 = a^2 + b^2\r<BR>\n" );
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document.write( "that's a given.\r<BR>\n" );
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document.write( "you also know that sin(A) = opposite / hypotenuse = a/c and cos(A) = adjacent / hypotenuse = b/c\r<BR>\n" );
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document.write( "in sin(A) = a/c, you can solve for a to get a = c * sin(A).\r<BR>\n" );
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document.write( "in cos(A) = b/c, you can solve for b to get b = c * cos(A).\r<BR>\n" );
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document.write( "in the formula c^2 = a^2 + b^2, you can replace a with c * sin(A) and you can replace b with c * cos(A) to get:\r<BR>\n" );
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document.write( "c^2 = (c*sin(A))^2 + (c*cos(A))^2\r<BR>\n" );
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document.write( "this becomes:\r<BR>\n" );
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document.write( "c^2 = c^2 * sin^2(A) + c^2 * cos^2(A)\r<BR>\n" );
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document.write( "divide both sides of this equation by c^2 and you get:\r<BR>\n" );
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document.write( "1 = sin^2(A) + cos^2(A)\r<BR>\n" );
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document.write( "QED\r<BR>\n" );
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document.write( "the definition of QED is:\r<BR>\n" );
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document.write( "QED is an abbreviation of the Latin words \"Quod Erat Demonstrandum\" which loosely translated means \"that which was to be demonstrated\". It is usually placed at the end of a mathematical proof to indicate that the proof is complete. </SPAN>\n" );
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