document.write( "Question 660148: The terminal side of angle θ in standard position contains the points (-5,-12) give the cos θ. \n" ); document.write( "
Algebra.Com's Answer #411065 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Hi, there--\r\n" );
document.write( "\r\n" );
document.write( "The Problem:\r\n" );
document.write( "The terminal side of angle θ in standard position contains the points (-5,-12) give the \r\n" );
document.write( "cos θ.\r\n" );
document.write( "\r\n" );
document.write( "Solution:\r\n" );
document.write( "We can find the cosine of an angle in a right triangle if we know the length of the adjacent \r\n" );
document.write( "side and the length of the hypotenuse.\r\n" );
document.write( "\r\n" );
document.write( "Angle θ is in Quadrant III because both x and y are negative. \r\n" );
document.write( "\r\n" );
document.write( "Since (-5,-12) is on the terminal side of the angle θ, we can draw a right triangle with \r\n" );
document.write( "angle θ at the origin. \r\n" );
document.write( "\r\n" );
document.write( "The hypotenuse of the triangle is the line segment from (0,0) to (-5,-12).\r\n" );
document.write( "\r\n" );
document.write( "The side adjacent to angle θ is the horizontal line segment along the x-axis between \r\n" );
document.write( "(0,0) and (-5,0). The directed side length is a=-5 units.\r\n" );
document.write( "\r\n" );
document.write( "The side opposite angle θ is the vertical line segment between (-5,0) and (-5,-12). The \r\n" );
document.write( "directed side length is b=-12 units.\r\n" );
document.write( "\r\n" );
document.write( "Use the Pythagorean Equation to find the length of the hypotenuse c.\r\n" );
document.write( "\r\n" );
document.write( "a^2 + b^2 = c^2\r\n" );
document.write( "(-5)^2 + (-12)^2 =c^2\r\n" );
document.write( "25 + 144 = c^2\r\n" );
document.write( "169 = c^2\r\n" );
document.write( "c = 13\r\n" );
document.write( "\r\n" );
document.write( "cos(θ) = [directed length of adjacent side] / [directed length of hypotenuse]\r\n" );
document.write( "cos(θ) = -12/13\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "If this is unclear, or you still have questions, please email me.\r\n" );
document.write( "\r\n" );
document.write( "Mrs. Figge\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
document.write( "
\n" ); document.write( "
\n" );