document.write( "Question 825898: If x = r sin A cos B and y = r sin A sin B and z = r cos A ,verify x^2 + y^2 + z^2 = r^2.\r
\n" ); document.write( "\n" ); document.write( "Thanks so much in advance:) \n" ); document.write( "
Algebra.Com's Answer #497725 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( "Given that \r\n" );
document.write( "x = r sin A cos B\r\n" );
document.write( "y = r sin A sin B\r\n" );
document.write( "z = r cos A\r\n" );
document.write( "\r\n" );
document.write( "Verify x^2 + y^2 + z^2 = r^2.\r\n" );
document.write( "\r\n" );
document.write( "A SOLUTION:\r\n" );
document.write( "Substitute r sin A cos B for x, r sin A sin B for y, and r cos A for z in the equation.\r\n" );
document.write( "\r\n" );
document.write( "x^2 + y^2 + z^2 = r^2\r\n" );
document.write( "(r sin A cos B)^2 + (r sin A sin B)^2 + (r cos A)^2 = r^2\r\n" );
document.write( "\r\n" );
document.write( "Simplify left-hand side.\r\n" );
document.write( "\r\n" );
document.write( "r^2 (sin A)^2 (cos B)^2 +r^2 (sin A)^2 (sin B)^2 + r^2 (cos A)^2 = r^2\r\n" );
document.write( "\r\n" );
document.write( "Factor r^2 from each term on the left-hand side.\r\n" );
document.write( "r^2 [ (sin A)^2 (cos B)^2 + (sin A)^2 (sin B)^2 + (cos A)^2 ] = r^2\r\n" );
document.write( "\r\n" );
document.write( "Factor (sin A)^2 from first two terms inside the brackets.\r\n" );
document.write( "\r\n" );
document.write( "r^2 [(sin A)^2 [(cos B)^2 + (sin B)^2] + (cos A) ^2 ] = r^2\r\n" );
document.write( "\r\n" );
document.write( "Simplify. (Recall that (cos B)^2 + (sin B)^2 = 1.)\r\n" );
document.write( "r^2 [(sin A)^2 + (cos A) ^2 ] = r^2\r\n" );
document.write( "\r\n" );
document.write( "Simplify again using same identity.\r\n" );
document.write( "r^2 = r^2\r\n" );
document.write( "\r\n" );
document.write( "VERIFIED!\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hope this helps! Feel free to email if you have any questions.\r\n" );
document.write( "\r\n" );
document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
document.write( "
\n" ); document.write( "
\n" );